Department of Physics • University of Cologne

Surface codes, leading candidates for quantum error correction (QEC) – and entanglement phases – a key notion for many-body quantum dynamics - have heretofore been unrelated. Here, we establish a link between the two. We map two-dimensional (2D) surface codes under a class of incoherent or coherent errors (bit flips or uniaxial rotations) to (1+1)D free-fermion quantum circuits via Ising models. We show that the error-correcting phase implies a topologically nontrivial area law for the circuit's 1D long-time state |ψ∞>. Above the error threshold, we find a topologically trivial area law for incoherent errors and logarithmic entanglement in the coherent case. In establishing our results, we formulate 1D parent Hamiltonians for |ψ∞> via linking Ising models and 2D scattering networks, the latter displaying respective insulating and metallic phases and setting the 1D fermion gap and topology via their localization length and topological invariant. We expect our results to generalize to a duality between the error-correcting phase of (d+1)D topological codes and d-dimensional area laws; this can facilitate assessing code performance under various errors. The approach of combining Ising models, scattering networks, and parent Hamiltonians can be generalized to other fermionic circuits and may be of independent interest.

For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. This talk will present the state-of-the-art in pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow of m-particle pseudofermion vertices. We will discuss the achievements of PFFRG in successfully predicting the spectroscopic signatures of candidate quantum spin liquid materials based on complex three-dimensional geometries with intricate Hamiltonians. These include the recently studied bi-trillium lattice S=1 K2Ni2(SO4)3 and the hyperhyperkagome lattice S=1/2 PbCuTe2O6 compounds. We also present the success of PMFRG in treating finite-temperature properties of three-dimensional systems by describing phase transitions and the associated critical exponents.

As first noted in [1], single-component fermionic polar molecules confined to two dimensions at sufficiently low temperatures form a topologically non-trivial px +ipy superfluid. For NaK, the critical temperature is theoretically predicted to be at around 15% of the Fermi temperature [2] and in our lab at MPQ we can currently reach temperatures as cold as 25%. It has been proposed in [3] to use blue-detuned tweezers to potentially braid Majoranas hosted at vortex cores in the px + ipy superfluid phase and also a topological qubit read-out scheme was suggested specific for ultracold molecules. Using these techniques it becomes feasible to build a prototype of a topological qubit, apply a gate operation by braiding Majoranas and measure the state of the qubit afterwards. This would directly show the non-Abelian character of the exchange of two vortices and thus provide a clear signature for the existence of Majoranas at their cores. Within this talk I will provide a detailed description of the experimental techniques necessary for such a prototypical topological qubit and outline its significance, but also the shortcomings mainly due to the finite lifetime of the superfluid making it unfortunately not immediately suitable for a full topological quantum computer. [1] N. R. Cooper and G. V. Shlyapnikov, “Stable topological superfluid phase of ultracold polar fermionic molecules,” vol. 103, no. 15, p. 155302. [2] F. Deng, X.-Y. Chen, X.-Y. Luo, W. Zhang, S. Yi, and T. Shi, “Effective potential and superfluidity of microwave-shielded polar molecules,” vol. 130, no. 18, p. 183001. [3] S. Tewari, S. Das Sarma, C. Nayak, C. Zhang, and P. Zoller, “Quantum computation using vortices and majorana zero modes of a p x + i p y superfluid of fermionic cold atoms,” vol. 98, no. 1, p. 010506.

I will discuss two problems: (i) observing measurement-induced collective phenomena, such as the measurement-induced entanglement transition, and (ii) testing the eigenstate thermalization hypothesis, which forms the basis of our understanding of thermalization in isolated many-body quantum systems. In the first case, standard experiments are not scalable because of the need to post-select on sets of measurement outcomes whose probabilities are exponentially small in the number of degrees of freedom. I will show that a different approach, which involves cross-correlating classical and quantum simulations, can be used to determine both upper and lower bounds on measurement-induced entanglement. This result shows that it is possible to efficiently and unambiguously observe measurement-induced collective phenomena. In the second case, a basic issue is that the theory of thermalization in isolated many-body quantum systems is formulated in terms of properties of eigenstates. At finite energy densities, many-body level separations are exponentially small, so in general we need exponential time to resolve eigenstates. I will show how the quantum search algorithm can be used to construct states having inverse polynomial energy width, as well as superpositions of such states. I will then discuss how, using these states, it is possible to formulate a test for violations of ETH that is valid in individual systems. Finally, I will show that detecting a violation of ETH using this test is a Quantum Merlin Arthur (QMA) problem.

As a new kind of topological order combining topology and geometry, fracton orders have attracted attentions from various domains for its theoretical novelty and potential implication for quantum information. The mobility of particles in fracton orders is restricted in lower dimensional subsystems of certain geometry, which is deeply rooted in novel entanglement patterns. In this talk, I will introduce a series of fracton ordered exactly solvable models which include not only point-like particles but also spatially extended excitations such that both mobility and deformability are restricted. We construct Hamiltonians, ground state wavefunctions and excitations, and study several exotic properties such as ground state degeneracies. We establish a program of entanglement renormalization for these fixed-point wavefunctions, rendering a hierarchy of entanglement patterns. Finally, I will demonstrate our exploration on subsystem symmetry protected topological orders, which are dual to fracton orders, focusing on the idea of strange correlators and generation of subsystem symmetries via higher-order cellular automata. The talk will be ended with several future directions.

Nonstabilizerness - commonly known as magic - quantifies resources beyond Clifford operations and is a fundamental resource for achieving universal quantum computation. Recently, several tensor network methods have been developed for computing the stabilizer Renyi entropy (SRE), a recently introduced measure of magic. These methods have unveiled intriguing insights into the behavior and properties of magic in many-body systems. In this talk, I will introduce a new approach to compute the magic, by representing the expectation values of Pauli strings as matrix product state (MPS). This method paves the way for calculating various measures of magic, including the SRE, the stabilizer nullity, and the Bell magic. Furthermore, it allows for extracting the stabilizer group of an MPS. Our method opens up the possibilty for exploring genuine magic within many-body systems.

Understanding and protecting against errors happening on a quantum device constitute one of the biggest challenges in developing a fault-tolerant quantum computing architecture. Recently, the focus of the community shifted from a static perspective, where information is encoded into a (fixed) subspace, to a dynamical perspective where one allows for the logical subspace to change over time [1], with the most famous example being Floquet codes, error-correcting protocols defined by a periodic sequence of low-weight non-commuting (Pauli) measurements [2]. Understanding and analyzing such protocols in the presence of errors is an important challenge to devise and to understand new fault-tolerant protocols. We argue that tensor network methods inspired by the ZX calculus are good tools to analyze the error-correction properties of dynamical protocols as they allow for a simple, graphical, yet complete understanding of the evolution of logical information through a circuit, also in the presence of errors [3]. In this talk, I want to give an introduction on how to represent circuits composed of Clifford unitaries and Pauli measurements graphically. First, I introduce the elementary tensors from which one can build tensor networks resembling the circuits of the above form. To understand error-correcting properties of a circuit expressed as a tensor network, I introduce the notion of *projective Pauli flow* in terms of projective symmetries of the building blocks of the network [4]. I will show how all quantities needed to perform error-correction on a circuit can be understood graphically as different types of Pauli flow. If time allows, I show how local relations amongst the elementary tensors can be used to ‘deform’ a circuit into a different, but equivalent one [3,5]. Importantly, these local deformations preserve the global Pauli flows and with that the logical action of the circuit and certain error-correction properties. This allows to transform given error-correcting circuits into new ones while preserving their error-correcting nature. [1] Delfosse, Paetznick; “Spacetime codes of Clifford circuits”, arXiv:2304.05943 [2] Hastings, Haah; “Dynamically Generated Logical Qubits”, arXiv:2107.02194 [3] Bombin et al; “Unifying flavors of fault tolerance with the ZX calculus”, arXiv:2303.08829 [4] Magdalena de la Fuente, Old, et al.; in preparation [5] Townsend-Teague, Magdalena de la Fuente, Kesselring; “Floquetifying the Colour Code”, arXiv:2307.11136

Interacting fermion ladders are important platforms to study quantum phases of matter including various Mott insulators with different symmetry properties, such as the D-Mott and S-Mott phase. The latter hold pre-formed electron pairs and become paired liquids (d-wave and s-wave) upon doping. These Mott insulators were believed to be distinct phases (see e.g. the classical textbook “Quantum physics in one dimension”). We demonstrate that this understanding is incomplete: They are in fact two facets of the same interaction-induced topological phase. With this, we provide a quantum analog of the well-known terminable liquid-gas transition. However, the phenomenology we uncover is even richer, as in contrast to the liquid-gas transition, the order of the transition can be tuned by the interaction and bears relevance for the topological properties of the system. These results show interesting synergy between fundamental questions in the fields of fermion pairing, topology, Mott insulators and terminated phase transitions.

Programmable Rydberg atom arrays stand out as extremely powerful platforms for the quantum simulation of strongly correlated states of matter. Their versatility lies in the adaptable geometry of the trapping lattice and in the wide variety of controllable atomic levels, which naturally yields several distinct interaction regimes. In a journey through the most recent theoretical and experimental achievements, I will show how these devices enable synthesizing and probing many-body states with topological order. Starting from the van der Waals-interacting regime, I will demonstrate that Rydberg Hamiltonians can host Z2 quantum spin liquids and analyze optimal protocols for their dynamical preparation. I will then introduce a novel class of Z3 spin liquids and engineer viable implementations in Rydberg atom setups. Finally, I will consider a system of 3-level atoms coupled via a time-reversal symmetry-breaking dipolar exchange interaction and provide numerical evidence for the emergence of gapped chiral spin liquids with the same form of topological order of the fractional quantum Hall effect.

Neural quantum states (NQS) are emerging as a versatile tool to tackle the quantum many-body problem. In particular, when dealing with correlated lattice models in intermediate spatial dimensions or with more complex interaction patterns, such as those occurring in molecules, NQS approaches have been shown to expand our computational capabilities. After introducing the basic ideas of the numerical machinery, I will give an overview of recent developments in the field.

Understanding how errors deteriorate the information encoded in a many-body quantum system is a fundamental problem with practical implications for quantum technologies. Here, we investigate a class of encoding-decoding random circuits with coherent errors. The existence of a phase transition separating an error-protecting phase at weak error strength from an error-vulnerable phase is analytically demonstrated. We derive exact expressions showing that this transition is accompanied by an area-to-volume law entanglement transition and a localization transition in the computational basis. The emergence of multifractal features in the considered system is highlighted.

Numerical calculations of the critical exponent of the localization length in the Chalker-Coddington (CC) model (\nu ~2.6) differ considerably from the experimental value (\nu~ 2.38) at the integer quantum Hall transition (IQHT). We review most of models considered recently, revile the origin of differences and the physics behind. The difference comes from the fact, that in CC model disorder of potential is not fully taken into account. Besides the phase factor disorder, coming from Bohm-Aharonov phase in the magnetic field, there is a structural disorder, connected with randomness of the position of saddle points of the random potential. At this points quantum tunneling is happening between Fermi lakes of the electrons in the potential landscape, which leads to change of localization length index \nu . We suggest, that interaction between electrons and atoms at the lattice sites affect disorder character of potential and, at the quasiclassical limit, on addition to U(1) phase disorder of CC model we have effective one particle random network model with structural disorder . In paper PRB.95, 125414 (2017) we propose a model for structural disorder, where numerical simulation on the basis of transfer matrix approach give a value \nu = 2.37 \pm 0.017, very close to the experimental value. Currently we have developed new technique of calculations and have launched new simulations of \nu based on S-matrix approach. Preliminary results confirm correctness of the value obtained earlier on basis of transfer matrix approach. We discuss also the role and validity of Harris criteria in a presence of structural disorder and argue, that the criteria should be modified.

Bachelor-Kolloquium

The Krylov complexity measures the spread of the wavefunction in the Krylov basis, which is constructed using the Hamiltonian and an initial state. In this work (arXiv:2303.12151), we investigate the evolution of the maximally entangled state in the Krylov basis for both chaotic and non-chaotic systems. Our findings suggest that neither the linear growth nor the saturation of Krylov complexity is necessarily associated with chaos. However, for chaotic systems, we observe a universal rise-slope-ramp-plateau behavior in the transition probability from the initial state to a Krylov basis, which is a characteristic of chaos in the spectrum of the Hamiltonian. Additionally, the long ramp in the transition probability is directly responsible for the late-time peak of Krylov complexity observed in previous literature. On the other hand, for non-chaotic systems, the transition probability exhibits a different behavior without the long ramp. Therefore, our results help to clarify which features of the wave function time evolution in Krylov space characterize chaos.

The 3D Ising transition, the most celebrated and unsolved critical phenomenon in nature, has long been conjectured to have emergent conformal symmetry, similar to the case of the 2D Ising transition. Yet, the emergence of conformal invariance in the 3D Ising transition has rarely been explored directly, mainly due to unavoidable mathematical or conceptual obstructions. Here, we design an innovative way to study the quantum version of the 3D Ising phase transition on spherical geometry, using the fuzzy (noncommutative) sphere regularization. We accurately calculate and analyze the energy spectra at the transition, and explicitly demonstrate the state-operator correspondence (i.e., radial quantization), a fingerprint of conformal field theory. In particular, we identify13 parity-even primary operators within a high accuracy and two parity-odd operators that were not known before. Our result directly elucidates the emergent conformal symmetry of the 3D Ising transition, a conjecture made by Polyakov half a century ago. More importantly, our approach opens a new avenue for studying 3D conformal field theories by making use of the state-operator correspondence and spherical geometry.

We develop an analytical approach to the study of one-dimensional free fermions subject to random projective measurements of local site occupation numbers, based on the Keldysh path-integral formalism and replica trick. In the limit of rare measurements, \gamma / J << 1 (where \gamma is measurement rate per site and J is hopping constant in the tight-binding model), we derive a non-linear sigma model (NLSM) as an effective field theory of the problem. Its replica-symmetric sector is described by a U(2) / U(1) x U(1) ~ S2 sigma model with diffusive behavior, and the replica-asymmetric sector is a two-dimensional NLSM defined on SU(R) manifold with the replica limit R -> 1. On the Gaussian level, valid in the limit \gamma / J -> 0, this model predicts a logarithmic behavior for the second cumulant of number of particles in a subsystem and for the entanglement entropy. However, the one-loop renormalization group analysis allows us to demonstrate that this logarithmic growth saturates at a finite value ~(J / \gamma)^2 even for rare measurements, which corresponds to the area-law phase. This implies the absence of a measurement-induced entanglement phase transition for free fermions. The crossover between logarithmic growth and saturation, however, happens at exponentially large scale, ln(l_corr) ~ J / \gamma. This makes this crossover very sharp as a function of the measurement frequency \gamma/J, which can be easily confused with a transition from the logarithmic to area law in finite-size numerical calculations. We have performed a careful numerical analysis, which supports our analytical predictions.

We have recently seen the emergence of quantum processors with more than 50 qubits. This has initiated a huge world-wide effort to utilize this new computational power. However so far it has not been that easy to extract the computational power promised in those quantum processors. Quantum neural networks has been seen as an approach, through which we might be able to facilitate these new quantum systems for computational tasks. In this seminar, I introduce several ideas with quantum neural networks and present a new quantum computational model which utilizes scale-free networks in the Hilbert space generated by the quantum processors. This quantum computational model is based on both reservoir computation and extreme machine learning and inherits their advantages. We discuss its potential and the advantages it provides.

A fundamental distinction between many-body quantum states are those with short- and long-range entanglement (SRE and LRE). The latter, such as cat states, topological order, or critical states cannot be created by finite-depth circuits. Remarkably, examples are known where LRE is obtained by performing single-site measurements on SRE states such as preparing the toric code from measuring a sublattice of a 2D cluster state. I will present a general framework of how and why these known protocols give rise to long range entanglement based on interpreting the cluster state measurement as implementing the non-local Kramers-Wannier transformation. This provides a scalable and practical way to 'gauge' a symmetry using only finite-depth circuits and measurements, and moreover allows us to go beyond the preparation of stabilizer states. In addition, we find a complexity hierarchy on long-range entangled states based on the minimal number of measurement layers required to create the state. I will argue that certain phases of matter cannot be prepared using any finite number of layers, while remarkably certain non-Abelian topological orders can be prepared in a single round of measurement. As an application, I will outline how current NISQ devices, such as Rydberg atom arrays and Google's quantum processors, can scalably prepare a large class of exotic phases such as non-Abelian topological order and even fracton phases. This talk is based on 2112.01519, 2112.03061, 2209.03964, and 2209.06202

The recent discovery of the family of AV3Sb5 (A=K, Cs, Rb) metals has sparked great interest in the study of kagome lattice systems. These materials exhibit a plethora of intriguing low-temperature behaviour, as superconductivity, a charge density wave (CDW) and time-reversal symmetry breaking (TRSB) without magnetic ordering have all been found within these compounds. Although much effort has been devoted to understanding the physics of these materials in the last few years, there are still many unknowns. For instance, the nature of TRSB is still unclear, as is the mechanism that stabilizes the CDW found. In this work, we study a model of interacting electrons on the kagome lattice at a mean-field level. In particular, both a single-orbital model and a multi-orbital extension are considered. Our calculations reveal the presence of different interaction-driven CDW patterns, with the single-orbital model exhibiting a CDW phase compatible with the experimental findings. Furthermore, no traces were found of TRSB without magnetic ordering nor of ferromagnetism, in accordance with recent variational Monte Carlo calculations. Our results also suggest that the px and py orbitals of the in-plane Sb atoms might not be crucial for determining the physical properties of AV3Sb5 materials, while the van Hove singularities in the band structure could be playing a key role in this regard.

In the past few years, van der Waals heterostructures have emerged as a new platform for studying frustrated magnetic systems, both in structures with layers exhibiting intrinsic magnetism, as well as "Hubbard model simulators" such as moiré transition metal dichalcogenides (TMD). I will first discuss bilayer U(1) Dirac spin liquids, with the homogenously stacked system being unstable towards spontaneous symmetry breaking. We show that adding a relative twist between the two layers softens the ordering instability, and the resulting ordered phase features a tuneable lattice of magnetic vortices. In the second part of my talk, I will present ongoing work on correlated insulating states at fractional fillings in moiré TMD bilayers, where the formation of self-organized charge lattices has been observed experimentally. We describe these ordered states and explore the possibility of spin-liquid states within a slave-rotor mean-field theory.

Device-independent quantum cryptography In this talk I will introduce the device-independent framework, and explain how the violation of a Bell inequality can be used to certify the security of cryptographic protocols. I will discuss how device-independent cryptography leads to security even when the underlying system and measurement setups are not well characterized or provided by an untrustworthy provider. Finally I will comment on the theoretical and experimental challenges and the progress in implementing device-independent quantum key distribution.

Integrable systems typically exhibit non-generic transport properties. The spin 1/2 Heisenberg model is particularly rich, with ballistic transport of energy and different regimes of spin transport, including ballistic, diffusive, and super-diffusive ones. I will discuss the fate of the diffusive and super-diffusive regimes under different types of Hamiltonian perturbations and show that symmetry of perturbations can play an important role. For example, perturbations that respect the SU(2) symmetry of the isotropic Heisenberg model can cause anomalous transport behaviour even away from exact integrability. In the second part, I will focus on Markovian perturbations and propose a new Krylov space-type approach for an efficient steady-state description of weakly driven and open, nearly integrable systems. Lindblad dissipator will be used to add the most necessary conservation laws iteratively and thus increase the interpretability of stabilized non-thermal steady states.

A remarkable feature of Weyl semimetals (WSMs) is Fermi arcs - anomalous surface states that connect Weyl nodes of opposite chirality. At the interface betweem two WSMs, they can instead connect Weyl nodes of the same chirality, leading to perfect transmission of electrons across the interface. In this talk, I will describe some recent work on the magnetic breakdown of electron transport in this setup. For an interface between WSMs twisted relative to one another, we show that a longitudinal magnetic field leads to a suppression of conductance owing to Landau-Zener tunneling between the interface modes of opposite chirality.

Quantum Repeaters for Quantum Communication Quantum channels enable the implementation of communication tasks inaccessible to their classical counterparts. The most famous example is the distribution of secret key. However, in the absence of quantum repeaters, the rate at which these tasks can be performed is dictated by the losses in the quantum channel. In practice, channel losses have limited the reach of quantum protocols to short distances. Quantum repeaters have the potential to significantly increase the rates and reach beyond the limits of direct transmission. This talk will provide a high-level overview of different types of the proposed quantum repeater architectures. We will then look at the specific techniques that these schemes utilise in order to achieve long distance quantum communication, analyse their strengths and limitations as well as discuss the required hardware needed to implement them. Finally, I will introduce a novel type of quantum repeater schemes which make efficient use of the quantum communication channels by encoding quantum information in the bosonic error-correcting codes.

Topological spin textures, such as two-dimensional skyrmion lattices (SkLs) and three-dimensional hedgehog lattices (HLs) are approximately represented by superpositions of multiple spin density waves, and hence, called multiple-Q spin textures. In such spin structures, the phase degree of freedom of the superposed waves plays an important role in the topological properties as well as the symmetry of the magnetic textures, but the systematic investigation has not been performed thus far. In this study, we theoretically investigate the evolution of magnetic and topological properties in SkLs composed of three spin density waves (3Q-SkL) and HLs composed of four spin density waves (4Q-HL) while changing the phases as well as the magnetization. By introducing a hyperspace to deal with the phases systematically, we find that the 3Q-SkLs change their skyrmion number among -2, -1, 0, 1, and 2 depending on the phase and magnetization. In the case of the 4Q-HLs, we clarify that the density and configuration of topological objects called hedgehogs and antihedgehogs change in a wide range. Our results provide good references to discuss how the actual systems experience the magnetic and topological transitions in an applied magnetic field.

Twisted moire materials have gained much attention since the recent discovery of superconductivity in twisted bilayer graphene. These materials offer an exciting new experimental platform to study the physics of strongly correlated electrons. The moire Hubbard model describes correlations in certain homobilayer twisted transition metal dichalcogenides. In this talk, I will present our recent results on the essential properties of this system. Using exact diagonalization and density matrix renormalization group methods, we find magnetic Mott insulating and metallic phases, which, upon doping exhibit intertwined charge and spin ordering and, in some regimes, pair binding of holes. The phases are highly tunable via an interlayer potential difference. Remarkably, the hole binding energy is found to be highly tunable revealing an experimentally accessible regime where holes become attractive. Moreover, I will present a novel approach to diagnosing superconducting Cooper condensation based on the structure of the two-body density matrix. I find that a superconducting condensate can be fragmented into partial condensates living on the charge stripes of a system. References: [1] Tunable Stripe Order and Weak Superconductivity in the Moire Hubbard Model, A. Wietek, J. Wang, J. Zang, J. Cano, A. Georges, A. Millis, Phys. Rev. Research 4, 043048 (2022) [2] Fragmented Cooper pair condensation in striped superconductors, A. Wietek, Phys. Rev. Lett. 129, 177001, Editors suggestion (2022)

Liquids are usually described within classical physics, whereas solids require the tools of quantum mechanics. I will show how in nanoscale systems this distinction no longer holds. At these scales, liquid flows may in fact exhibit quantum effects as they interact with electrons in the solid walls. I will first discuss the quantum friction phenomenon, where charge fluctuations in the liquid interact with electronic excitations in the solid to produce a hydrodynamic friction force. Using many-body quantum theory, we predict that this effect is particularly important for water flowing on carbon-based materials, and we obtain experimental evidence of the underlying mechanism from pump-probe terahertz spectroscopy. I will then show how the theory can be pushed one step further to describe hydrodynamic Coulomb drag - the generation of electric current by a liquid in the solid along which it flows. This phenomenon involves a subtle interplay of electrostatic and electron-phonon interactions, and suggests strategies for designing materials with low hydrodynamic friction.

Floquet or periodically driven systems show topological phases that are qualitatively different from their static counterparts. In this talk I will first introduce the new kinds of topological phases that can be realized in free-fermion Floquet systems. I will then show that the edge modes encountered in certain free fermion Floquet systems are remarkably robust to adding interactions, even in disorder-free systems where generic bulk quantities can heat to infinite temperatures due to the periodic driving. This robustness of the edge modes to heating can be understood in the language of strong modes for free fermion chains, and almost strong modes for interacting chains. I will then outline a tunneling calculation for extracting the long lifetimes of these edge modes by mapping the Heisenberg time-evolution of the edge operator to dynamics of a single particle in Krylov subspace.

I will discuss the effects of local measurements on critical quantum ground states. These states are highly entangled and feature algebraic correlations between local observables. As a consequence, local measurements can have highly nonlocal effects. Our focus is on Tomonaga-Luttinger liquid (TLL) ground states, a continuous family of critical states in one dimension whose structure is parameterized by a Luttinger parameter K. We show that arbitrarily weak local measurements, performed over extended regions of space, can conspire to drive transitions in long-wavelength correlations. Conditioning first on a particular measurement outcome we show that there is a transition in the character of the resulting quantum state for K<1, and highlight a formal analogy with the effect of an impurity on transport. To study the full ensemble of measurement outcomes we consider averages of physical quantities which are necessarily nonlinear in the system density matrix. We show how their behaviour can be understood within a replica field theory, and for the measurements that we consider we find that the symmetry of the theory under exchange of replicas is broken for K<1/2. For K<1/2 there is a suppression of quantum fluctuations of measured observables which becomes more prominent at long wavelengths.

Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly non-trivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive a competition between various ground states, such as charge density wave order and superconductivity. In this work, we study an electronic model of topologically-trivial flat bands with a continuously tunable Fubini-Study metric in the presence of on-site attraction and nearest-neighbor repulsion, using numerically exact quantum Monte Carlo simulations. By varying the electron filling and the spatial extent of the localized flat-band Wannier wavefunctions, we obtain a number of intertwined orders. These include a phase with coexisting charge density wave order and superconductivity, i.e., a supersolid. In spite of the non-perturbative nature of the problem, we identify an analytically tractable limit associated with a `small' spatial extent of the Wannier functions, and derive a low-energy effective Hamiltonian that can well describe our numerical results. If time permits, I will also discus some preliminary quantum Monte Carlo results for twisted bilayer graphene at charge neutrality.

Topological phases of matter have been the subject of intense interest since the discovery of the fractional quantum hall effect. More recently they have come to underpin leading approaches to quantum error correction. To date, the focus has remained on topological phases in two dimensions and the anyon models that describe them. In three dimensions our understanding is significantly less developed, the existence of immobile quasiparticles known as fractons opens up a landscape of intricate possibilities. The immobility of fractons leads to new possible symmetry actions, subdimensional phase transitions, and glassy dynamics that can be harnessed to produce more robust quantum codes. In this talk I will give an overview of recent efforts to develop a systematic understanding of fracton topological phases and what this might tell us about three dimensional topological codes.

Frustrated three dimensional quantum magnets bear a rich phenomenology but are notoriously hard to treat theoretically. We show how a Majorana representation of spin operators, in combination with the functional renormalization group allows for quantiative simulations at finite temperatures. Focusing on Heisenberg magnets, we establish a finite-size scaling approach and extract accurate results for critical temperatures and -exponents. Further, we quantify and discuss the improvements introduced by two-loop contributions in the flow equations applied to the Pyrochlore lattice. We then investigate the accuracy of its prominent spin-ice rule under the influence of both quantum and thermal fluctuations.

With rapid progress across platforms for quantum systems, the problem of many-body quantum state reconstruction for noisy quantum states becomes an important challenge. There has been a growing interest in approaching the problem of quantum state reconstruction using generative neural network models. In this talk, I will present the 'attention-based quantum tomography' (AQT), a method of quantum state reconstruction that uses an attention mechanism-based generative network. The results demonstrate not only that AQT outperforms earlier neural-network-based quantum state reconstruction on identical tasks but that AQT can accurately reconstruct the density matrix associated with a noisy quantum state experimentally realized in an IBMQ quantum computer. In addition, I will highlight broader applications of AQT currently being developed.

Engineering flat electronic bands from first mathematical principles Alexander Kruchkov Institute of Physics, EPFL, Lausanne, Switzerland Department of Physics, Harvard University, USA Branco Weiss Society in Science, ETH Zurich, Switzerland The concept of flat electronic bands is a change of paradigm in condensed matter physics. In this talk, I will address the origin of band flatness and its connection to the quantum geometry of electronic states.1 My work focuses on engineering the flat topological bands from the first mathematical principles, namely the Riemannian metrics and quantum geometry, with consequent holomorphicity and meromorphicity of the flat band states,1,2,3 enforced with accurate atomistic compu­ tations, DFT and tight binding with lattice relaxation effects.4,5 It provides deep insights on the origin of band flatness, which should be looked for in the real space (rather than in momentum space as conventionally it had been). In the complicated and messy domain of band structure computations, the developed approach provides an aesthetical tool for engineering flat electronic bands in realistic materials4 with consequent experimental confirmation.6,7 Time permitting, I will address the novel formalism of flat­band quantum transport built on the concepts of quantum geometry.8 References: [1] A. Kruchkov, Origin of band flatness and constraints of higher Chern numbers, arXiv 2105.14672 (2021). [2.] G. Tarnopolsky, A. J. Kruchkov, A. Vishwanath, Origin of magic angles in twisted bilayer graphene, Physical Review Letters 122, 106405 (2019). [3.] E. Khalaf, A. J. Kruchkov, G. Tarnopolsky, A. Vishwanath, Magic angle hierarchy in twisted graphene multilayers, Physical Review B 100, 085109 (2019). [4.] S. Carr, C. Li, Z. Zhu, E. Kaxiras, S. Sachdev, A.J. Kruchkov, Ultraheavy and ultrarelativistic Dirac quasiparticles in sandwiched graphenes, Nano Letters (2020). [5.] F. Haddadi, Q. Wu, A. J. Kruchkov, O.V. Yazyev, Moiré flat bands in twisted double bilayer graphene, Nano Letters (2020). [6.] J.M. Park, Y. Cao, K. Watanabe, T. Taniguchi, P. Jarillo­Herrero, Tunable strongly coupled superconductivity in magic­angle twisted trilayer graphene, Nature volume 590, (2021). [7.] Z. Hao, A. M. Zimmerman, P. Ledwith, E Khalaf, D. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath, P. Kim, Electric field–tunable superconductivity in alternating­twist magic­angle trilayer graphene, Science 371, 6534 (2021). [8.] A. Kruchkov, Quantum transport in dispersionless electronic bands, in preparation (2021).

Open quantum systems are ubiquitous in the contexts of atomic and molecular physics, circuit QED and optomechanics. Couplings to an environment can also have very interesting effects on the dynamics of many-particle quantum systems. In order to arrive at a tractable description of such problems, it is customary to work within the Markovian approximation, whereby the system is described by a Lindblad master equation. While much progress has been made in analysing Lindblad equations for many-particle systems by employing, for example, perturbative and matrix product states methods, it is clearly highly desirable to have exact solutions in specific, and hopefully representative, cases. This talk aims to show that for a number of interacting open quantum systems, it is possible to obtain exact analytic solutions through a connection with integrable models. I will describe how a correspondence between a Lindblad equation and an integrable Hamiltonian can be established and what information about the open systems it provides. In particular, I will discuss the equivalence in structure of generalised Hubbard models and vectorised Lindblad equations, which are already visible in the R-matrix of the integrable model. I will also mention how this construction can be extended by focusing purely on the integrability of the invariant subspaces of the Lindblad equations. The talk is based on the work presented in SciPost Phys. 8, 044 (2020) (doi: 10.21468/SciPostPhys.8.3.044).

Environmental coupling typically drives a quantum system to a unique steady state with very little coherence, which is a major obstacle for quantum information processing. I will talk about a simple experimental setting of an array of two-level systems with localised pump and loss that has multiple highly coherent steady states, including maximally entangled states of nonlocal Bell pairs. Such states originate from a hidden symmetry that conserves Bell pairs over long distances, leading to controllable long-range entanglement. I will discuss how to selectively prepare and observe these states in a broad range of present-day setups.

The talk is in three parts. Part 1: Universal spectral signatures of many-body-localization The notion of universality is enormously powerful in understanding equilibrium phases and phenomena. At the most practical level, it allows us to substitute a complicated problem for a much simpler one. A surprising notion of universality has been observed for quantum chaotic systems, which are said to constitute a non-equilibrium 'eigenstate phase' of matter. Correlations in the spectrum are observed to be reproduced by a particularly simple system- random matrix ensembles, which predict universal signatures, such as a `ramp' in the spectral-form-factor. I will argue the existence of analogous universal signatures for a different eigenstate phase constituted by many-body-localized systems. Based on joint work with Manas Kulkarni (ICTS-TIFR) and Jedediah Pixley (Rutgers). Part 2: Eigenstate phases with non-Abelian symmetry. A long-standing open question is whether there exist any eigenstate phases beyond the now-well-known examples of many-body-localized or quantum-chaotic systems. A promising possibility presents itself for systems with finite non-Abelian symmetries. By numerically studying a spin-chain with such a symmetry in the presence of disorder, we see some evidence for the presence of a novel eigenstate phase of matter. Based on joint work with Tzu-Chieh Wei (Stony Brook), Sriram Ganeshan (CCNY) and Lukasz Fidkowski (University of Washington). Part 3: Emergent supersymmetry in fermionic symmetry-protected-topological phases. Symmetry-protected topological phases are characterized by an almost trivial insulating bulk but exotic boundaries due to the presence of 't Hooft anomalies. These anomalies present themselves in manifold ways- protected gapless phases, Landau-forbidden deconfined quantum critical transitions and the absence of a trivial order. I will demonstrate that for a large class of fermionic SPT phases, the boundary anomaly presents itself in a fascinating manner- emergent supersymmetry with no fine tuning of any kind! This might present the most robust realization of supersymmetry in solid-state and cold atomic systems. Based on joint work with Juven Wang (Harvard)

It has been predicted that topological magnon insulators are realized in kagome plane of pyrochlore magnetic insulators with Dzyaloshinskii-Moriya interaction. Bosonic topological insulators can exhibit a topological band structure. Although bosonic system ground state is trivial condensate or the vacuum, their excited states may carry signatures of the topology. In this presentation, I will show the distinct features of excitations in kagome lattice within the framework of the spin-wave theory: (a) finite lifetime at zero temperature due to spontaneous two-magnon decays, (b) the renormalization of magnon energy depending on the magnetization direction, (c) singularities in the decay rate. Those features are shown in the form of dynamical structure factors. Their effect in experimentally detecting edge modes will also be discussed.

The characterization of quantum chaos in many-body systems has been an active area of research in the past several years. There have been several proposed diagnostics of quantum chaos, like the out-of-time-ordered correlators and the spectral form factor, to name a few. The focus of this talk is another quantity known as the operator entanglement. A particularly interesting measure of operator entanglement is the tripartite operator mutual information which is a quantitative measure of the amount of information delocalization. By studying the tripartite operator mutual information of both unitary operators and local operators in a variety of systems ranging from conformal field theories to spin chains, we demonstrate the utility of operator entanglement in distinguishing chaotic and non-chaotic theories.

Typically, a generic quantum many-body system under isolation is known to thermalize. However, there are exceptions where thermalization is violated. For instance, while a strong violation of thermalization occurs in the well known many-body localizing systems (MBL), a violation in the weaker sense occurs through the phenomenon of quantum many-body scars (QMBS). In this talk, I will first review both MBL and QMBS. I will then describe our recent work where we showed that an emergent symmetry in a single eigenstate of a disordered model protects it from MBL while not preventing the rest of the states in the spectrum from many-body localizing. I will motivate how such an example calls for exploring "inverted quantum scars", namely, non-area law states embedded in a spectrum of localized states. Time permitting, I will also walk you through our other recent works where we construct topologically ordered scarred models.

Much insight has come from the idea that non-equilibrium systems can exhibit phenomena not found in thermal equilibrium. Understanding these non-equilibrium phases and the transitions between them is a major research frontier of modern many-body physics. In my talk I will outline two examples of novel physics found in non-equilibrium quantum systems. The first, discrete time crystals (DTCs), are a prototypical example of a non-equilibrium phase of matter, defined by the fact that they spontaneously break time-translation symmetry. I will describe the results of an experiment involving the observation of a DTC in a doped semiconductor platform, where both interactions and dissipation play a significant role in stabilizing the DTC order. Next I will discuss measurement-induced transitions, which are a new class of phase transition in open quantum systems. I will focus on two aspects of these transitions: the effect of the underlying unitary dynamics on the nature of the phase transition, and the role of dimensionality in determining the universal properties at criticality.

As a potential window on transitions out of the ergodic, many-body-delocalized phase, we study the dephasing of weakly disordered, quasi-one-dimensional fermion systems due to a diffusive, non- Markovian noise bath. This bath is generated by inelastic scattering due to short-ranged interactions. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling. However, we find that instabilities in the calculation signal a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interactions perturbatively and the Coulomb interaction exactly. The latter provides a physical infrared regularization that stabilizes perturbation theory at long times, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. Our results are relevant to the search for precursors to the MBL transition that can be understood in the high-T ergodic phase. As a bonus, the calculation also provides a mechanism for the enhancement of dephasing at low temperatures in spin SU(2)-symmetric quantum wires, beyond the Altshuler-Aronov-Khmelnitsky result. The enhancement is possible due to the amplification of the triplet-channel interaction strength, and provides an additional mechanism that could contribute to the experimentally observed low-temperature saturation of the dephasing time.

In this presentation, the emergence of localised, stable wave packets (solitons) is investigated in the context of the repulsive one-dimensional Bose gas. In the weakly interacting limit, the gas is approximated by the classical non-linear Schrödinger equation, of which it is known that such classical localisation occurs. A natural question to ask would be whether these classical wave packets could be reproduced starting from the quantum non-linear Schrödinger equation, and if so, which quantum mechanical wave function would produce such density profiles. Previous research has indeed attempted to do so, however, these studies had two main limitations: 1) only the attractive regime was investigated, which has limited physical significance because there is no saturation, and 2) localisation was shown only in limiting cases. In the talk, some of the mathematical steps are outlined in an attempt to overcome these two shortcomings. Besides introductory material, the talk is split into three parts according to the results obtained: 1) numerical results are discussed that show whether the desired localisation even exists outside the weakly interacting regime, 2) analytical efforts are discussed that show that Dirichlet kernels arise from the density form factor and finally 3) I will share some of the analytical efforts on simplifying general density form factors, which are of relevance when comparing magnitudes between form factor terms. It is found that mutually repulsive particles experience attraction at the macroscopic level, outside of the weakly and maximally interacting limits.

Spins can be represented in terms of complex fermionic operators. This allows for a direct application of many-body techniques like the functional RG approach to frustrated quantum magnets. However, as the representation above introduces unphysical Hilbert space sectors, the applicability of this approach at finite temperatures is questionable. Here, I review an alternative Majorana fermion representation of spins which does not introduce any unphysical states. We develop a general functional RG formalism for Majoranas and apply it to the Pseudo-Majorana representation of Heisenberg models on small spin clusters as well as frustrated square and triangular lattices. We compute the finite temperature behavior of spin correlations and thermodynamic quantities and compare to exact diagonalization and the high-temperature series expansion.

Machine learning is becoming widely used in analyzing the thermodynamics of many-body condensed matter systems. Restricted Boltzmann machine (RBM) aided Monte Carlo simulations have sparked interest recently, as they manage to speed up classical Monte Carlo simulations. In the talk, based on my recently published paper (Phys. Rev. B 102, 195148), I will explain how we used the convolutional restricted Boltzmann machine (CRBM) method to reduce the number of parameters to be learned drastically by taking advantage of translation invariance. Furthermore, I will show that it is possible to train the CRBM at smaller lattice sizes, and apply it to larger lattice sizes. To demonstrate the efficiency of CRBM, I show the application to the Ising and honeycomb Kitaev models.

The Kitaev honeycomb model is well-known to host a quantum spin liquid at zero temperature, exhibiting topological order and fractionalization of spin into emergent Majorana fermion minimally coupled with Z2 gauge field. The exact solvability of this model stems from the conservation of local gauge fluxes, which also has dramatic impact upon the nonequilibrium dynamics when the system is brought out of equilibrium and isolated from any environment. The latter issue has been widely studied in the quest of emergent ergodicity in generic quantum manybody systems, or ergodicity breaking in manybody localization or other mechanisms. In this talk, I will show that the homogeneous Kitaev model exhibits the phenomenon of disorder-free localization, where the fractionalized Majorana fermion is partially localized by the Z2 gauge flux disorder dynamically generated in a highly excited state. As a result, the system exhibits exotic quench dynamics that is neither MBL nor ergodic: (1) algebraic lightcone of dimer correlation spreading; (2) algebraic decaying critical correlation in late time steady state; (3) algebraic growth of projective bipartite entanglement entropy to a volume law. Further, I will show numerical evidence that the long time feature is stable against solvability breaking perturbation. Our results may possibly imply nontrivial dimer correlation for Kitaev spin liquids at finite temperature.

In this talk, I will show that the defects of the valence plaquette solid(VPS) order parameter, in addition to possessing non-trivial quantum numbers, have fracton mobility constraints in the VPS phase. The spinon inside a single vortex cannot move freely in any direction, while a dipolar pair of vortices with spinon pairs can only move perpendicular to its dipole moment. These mobility constraints, while they persist near QCP, can potentially inhibit the condensation of spinons and preclude a continuous transition from the VPS to the Néel antiferromagnet. Instead, the VPS melting transition can be driven by the proliferation of spinon dipoles. In particular, we argue that a 2d VPS can melt into a stable gapless phase in the form of an algebraic bond liquid with algebraic correlations and long-range entanglement. Such a bond liquid phase yields a concrete example of the elusive 2d Bose metal with symmetry fractionalization.

Kitaev proposed an interacting model of spins (1/2) on a honeycomb lattice exactly solvable by mapping onto free Majorana fermions coupled to a Z_2 gauge field, hosting vortices (pi flux in a hexagon). In the presence of a time-reversal symmetry-breaking term, the ground state is gapped, characterized by a Chern number v in Z and the system hosts anyonic excitations. The Chern number ν mod 16 specifies the type of anyonic excitations, hence the sixteen-fold way. Our investigation in many well-chosen triangular vortex configurations (and their duals) shows 14 out of 16 of these phases. The phases with v = +-7 are missing. In a general case, we prove that any periodic vortex configuration with an odd number of vortices per geometric unit cell can only host even Chern numbers whereas odd Chern numbers can be found in other cases. Reference: J.N. Fuchs, S. Patil, J. Vidal, https://arxiv.org/abs/2005.03655 People interested in chatting with the speaker please let it know to Matteo Rizzi, who will organize a schedule accordingly.

The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose experimental exploration is currently pushed forward using quantum simulators. In this talk I will discuss our recent efforts towards the development of versatile variational approaches, which are efficiently applicable also to two-dimensional systems. On the one hand, a perturbatively motivated variational ansatz enabled us to identify disorder-free localization in an interacting two-dimensional lattice gauge theory [1]. On the other hand, leveraging large scale computational resources, we were able to demonstrate that neural network wave functions can exceed the capabilities of tensor networks on the task of computing quench dynamics in the two-dimensional quantum Ising model [2]. [1] P. Karpov et al., arXiv:2003.04901 [2] M. Schmitt and M. Heyl, arXiv:1912.08828

Abstract: A major goal for theoretical physics is the unification of gravity with quantum mechanics. An important tool for tackling this question is holography, or the duality between a theory of gravity and a conformal field theory in one lower dimension. In this talk I will address the question of how to reconstruct the geometry of a gravitational spacetime with field theoretic tools, relying on observables such as Wilson lines that are amenable to quantization. I will invoke a varied toolkit drawing on techniques from many areas of physics and mathematics, from quantum information to symplectic geometry. Importantly, my focus will be on de Sitter spacetime, which closely resembles our actual universe, and whose quantization could give insight into non-perturbative phenomena in cosmology.

A major goal of modern physics is to understand and test the regime where quantum mechanics and general relativity both play a role. However, its distinctive effects are typically relevant at high energies or strong gravitational fields, beyond the reach of present-day experiments. In this seminar I will discuss a different approach, focused on low-energy but composite quantum systems. Internal dynamics of composite systems can act as a sensitive probe of relativistic effects even at low-energies and in weak gravitational fields -- I will explain what quantum and general relativistic effects can arise for such systems and how they can be tested. I will outline the broader relevance of this approach for the research on joint foundations of quantum mechanics and general relativity, and for the future quantum-enhanced technologies such as metrology and sensing, or information processing.

There is evidence that spacetime and gravity emerge from the dynamics of more fundamental, strongly coupled degrees of freedom. The most concrete realization of this idea is the AdS/CFT paradigm, where gravity is holographically encoded in the physics of certain conformal field theories. I will describe some of my contributions towards understanding fundamental aspects of AdS/CFT, in particular the search for the dual description of the volume of the emergent space, and general results about chaos and the quantum butterfly effect in strongly coupled quantum systems.

In this talk, I will review the recent advances in the understanding of intriguing infinite-dimensional symmetries that emerge at the boundary of spacetimes. These symmetries play an important role in the description of many phenomena such as gravitational memory effects, scattering amplitudes in flat space and black hole physics. By connecting seemingly unrelated topics in theoretical physics, infinite-dimensional symmetries have shed a new light on the fascinating universal features of gauge theories and gravity.

In the search for a theory of quantum gravity that is able to resolve singularities in classical general relativity and explain the first moments of the universe, string theory delivers powerful tools: the “holographic” AdS/CFT duality allows us to study quantum gravity using much better understood field theory methods. I will explain some of the progress towards an explicit decoding of relevant aspects of gravity from a holographic quantum field theory. I will particularly focus on the emergence of spacetime dynamics from quantum entanglement, and on a new way to think about quantum chaos which serves as a useful diagnostic of black hole physics.

I will present three mechanisms for emergence of gravity from 2D conformal field theory (CFT). Two of them are based on entanglement, exemplifying the intricate relation between quantum information and quantum gravity, and one on a deformation of the CFT with an irrelevant operator. While the context of this work is holography, the mechanisms themselves are non-holographic. The resulting gravitational system is of direct relevance to the set-up used in recent papers reporting significant progress on the black hole information paradox

Recently, three-dimensional topological spin textures called the magnetic hedgehog lattices (HLs) were discovered in the B20-type compounds MnSi1-xGex [1]. The HLs have periodic arrays of magnetic monopoles and anti-monopoles, which induce interesting transport phenomena, such as the topological Hall effect and the topological thermoelectric transport. However, their stabilization mechanism has not been fully understood thus far. Here we investigate the ground state of an effective spin model with long-range interactions arising from the itinerant nature of electrons by variational calculations and simulated annealing. We find that the HLs are stabilized even at zero field by the synergetic effect of symmetric and antisymmetric interactions from the spin-charge and spin-orbit couplings, respectively. We clarify the full phase diagram in the magnetic field, which includes multiple phase transitions with changes in the number of monopoles and anti-monopoles [2]. We also find that the monopoles and anti-monopoles move, repel, and pair annihilate with topological phase transition by increasing the magnetic field successively [3]. [1] Y. Fujishiro et al., Nat. Commun. 10, 1059 (2019). [2] S. Okumura, S. Hayami, Y. Kato, and Y. Motome, arXiv:1908.05044. [3] S. Okumura, S. Hayami, Y. Kato, and Y. Motome, arXiv:1909.01316.

We study the quantum propagation of a skyrmion in chiral magnetic insulators by generalizing the micromagnetic equations of motion. The fluctuations around the skyrmionic configuration give rise to a damping derived microscopically, which in some limit reduces to a skyrmion mass. We demonstrate that a skyrmion in a confined geometry behaves as a massive particle, a discovery with great impact on the technologically important case of linear tracks relevant for magnetic memory devices. In the presence of time-dependent oscillating magnetic field gradients, the unavoidable coupling of the external field to the magnons gives rise to time-dependent dissipation for the skyrmion, with measurable consequences on the skyrmion path. These ac fields act as a net driving force on the skyrmion via its own intrinsic magnetic excitations. We generalize the standard quantum theory of dissipation to include the stochastic effects of the driven bath on the skyrmion dynamics. Our work initiates studies towards the possibility of observing a quantum mechanical behavior at a mesoscopic scale. I will briefly talk about the observability of tunneling events, in particular quantum depinning of a magnetic skyrmion out of a pinning center.

Driven-dissipative systems can potentially exhibit non-equilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions present in these systems generically exhibit an effectively classical, equilibrium behavior in spite of their non-equilibrium origin. In this talk, I investigate an experimentally motivated model where two Ising-like order parameters interact and form a multicritical point. I will discuss how at such a multicritical point, new non-equilibrium criticality can emerge. These non-equilibrium multicritical points exhibit a variety of exotic phenomena with no counterpart in equilibrium, including spiraling phase boundaries, the emergence of discrete scale invariance rather than the more familiar continuous scale invariance, and the violation of the fluctuation-dissipation theorem at all length scales, resulting in a sytem which becomes “hotter” and “hotter” at longer and longer wavelengths. Furthermore, I will discuss how for more complex order parameters with a different form of symmetry, additional non-equilibrium multicritical points can emerge.

In magnetically ordered systems, fluctuations on top of the ordered state in the form of magnons can induce effective interactions. These magnon-mediated interactions may act to stabilise exotic phases of matter, and also significantly contribute to non-equilibrium responses. I will discuss two recent examples. Numerical results provide evidence for the existence of a partially disordered ground state in the antiferromagnetic stuffed honeycomb lattice, in which collinearly ordered moments coexist with an only short-range correlated subsystem. I show how magnons in the ordered honeycomb system mediate interactions among the central spins and derive an effective model. Fluctuations near the transition between two competing ground states of the model are conjectured to lead to a quantum disordered ground state. I will further discuss how magnon interactions are crucial for the optical generation of coherent magnons in easy-plane antiferromagnets, with a particular focus on the spin-orbit Mott insulator Sr2IrO4. Here, laser fields which directly couple to the local moments induce effective fields which drive a low-energy magnon, giving rise to a finite out-of-plane magnetization. The subsequent dynamics can be probed using a pump-probe protocol.

Electrical and thermal conductances of a quantum Hall bar reflect the topological structure of the incompressible bulk phase. Here we show that noise of electrical current carried through the edge evidences the interplay between these two topological observables. Transport through an edge of particle-hole conjugate states is modeled by a voltage-biased line junction made up of counter-propagating modes. Specifically, we focus on the edge of a \nu = 2/3 fractional quantum Hall state. Noise is generated at a point distinctly separated from the hot spot (where most of the Ohmic dissipation takes place) and reflects the competition between ballistically carried downstream current and diffusively carried heat (which can propagate also upstream). We propose specific setups where our predictions can be measured.

I will review recent developments of transport in materials with a very small overlap between the bottom of the conduction band and the top of the valence band. I will focus on hydrodynamic and kinetic manifestations of chiral anomalies. After introducing basic theoretical concepts I will discuss relativistic Weyl particles. Next I will introduce materials, the so-called multi-Weyl semi-metals, which do not have relativistic dispersion yet are anomalous at the quantum level. Finally, I will present recent developments and challenges in measuring hydrodynamic transport of electrons in semi-metals.

An exact formula for the temperature dependent Hall number of metals is derived. It is valid for nonrelativistic fermions or bosons, with an arbitrary potential and interaction. This dc transport coefficient is proven to (remarkably) depend solely on equilibrium susceptibilities, which are more amenable to numerical algorithms than the conductivity. An application to strongly correlated phases is demonstrated by calculating the Hall sign in the vicinity of Mott phases of lattice bosons.

In the past decade we have witnessed enormous progress in experiments that consist of placing magnetic atoms at predetermined positions on substrates and building magnetic nanostructures, one atom at a time. The interactions between magnetic moments are mediated by the conduction electrons through a mechanism understood in terms of a theory developed decades ago by Ruderman, Kittel, Kasuya, and Yosida, dubbed "RKKY theory", which applies when the spins are classical. The quantum nature of the electronic spin introduces another degree of complexity and competition with other quantum phenomena: the Kondo effect. This competition is quite subtle and non-trivial, and can only be studied by numerical means. We explore these phenomena on different lattice geometries in 1,2 and 3 dimensions by introducing an exact mapping onto an effective one-dimensional problem that we can solve with the density matrix renormalization group method (DMRG). We show a clear departure from conventional RKKY theory and important differences that can be attributed to dimensionality and geometry. In particular, for the square and cubic lattices at half filling, Kondo physics dominates even at short distances, while the ferromagnetic RKKY state is energetically unfavorable, translating into a finite range for the RKKY interaction. In the case of larger spin S=1, RKKY correlations can coexist with (partial) screening.

Quantum Monte Carlo (QMC) methods, when applicable, offer dependable ways to extract the nonperturbative physics of strongly-correlated many-body systems. However, there are some formidable bottlenecks to the applicability of these methods such as the sign problem and algorithmic update inefficiencies. Using the t-V model Hamiltonian, I demonstrate how the fermion bag approach--originally developed in the context of Lagrangian lattice field theories--led to the first sign problem solution for this model. I then show how using fermion bag ideas to develop a new efficient QMC algorithm to study the t-V model allowed us to compute critical exponents for the chiral Ising universality class (involving one flavor of four-component Dirac fermions) that seem to be more reliable than those from previous QMC calculations. Finally, I discuss how the fermion bag approach offers certain advantages to the study of other models involving Dirac fermions and also extends to fermion-spin interactions and Z_2 gauge theories.

We study the relationship between the physics of topology and zero modes in frustrated systems and metamaterials. Zero modes that exist in topological matters are distinct from the ones arising from symmetry breaking. Incidentally, a prominent aspect of frustrated systems and metamaterials also is to harbor such kind of zero modes in form of an accidental degeneracy. Taking cues from these two apparently different phenomena, we ask a simple question: are the robust features of frustration topologically protected and if so can we classify different types of frustration using topology? In answering these questions we invoke the tools of topological mechanics to identify the key agent at play, namely the rigidity matrix, which is a non-Hermitian matrix and decides the topology of spin-wave zero modes in a frustrated magnet or phonon modes in metamaterials. Further developments of the theory rely on combining the recent developments in our understanding of Maxwell constraint counting and generalizing the ten-fold way classification of Hermitian matrices to non-Hermitian matrices. The result is a three-fold way classification for each Maxwell counting index. We illustrate the classification by demonstrating the existence of a new vortex-like invariant for real rigidity matrices using random matrices and through example frustrated spin models. So by classifying all the rigidity matrices, we answer the question of the origin of frustration (i.e. zero modes in the form of accidental degeneracy) in a wide class of frustrated magnets and metamaterials by linking it to topological invariants.

An electronic Ising-nematic order spontaneously breaks the rotation symmetry of the underlying lattice down to two-fold. It has been observed in various systems, in particular the cuprate and iron-based high temperature superconductors. In the vicinity of a nematic quantum critical point — achieved by tuning some external parameter such as pressure or doping — the physics is described by that of low-frequency long-wavelength order parameter fluctuations coupled to a Fermi surface. However, due to the momentum-conserving nature of the induced electron-electron interaction, the temperature dependence of the resistivity near an Ising nematic QCP remains unclear. In this talk, we shed light on the problem by incorporating disorder and Umklapp process into the low-energy theory. Our work can be viewed as solving an extended Boltzmann equation, with a collision integral that accounts for complicated multi-particle scattering processes important near the QCP.

We developed general approach to the calculation of power-law infrared asymptotics of spin-spin correlation functions in the Kitaev honeycomb model with different types of perturbations. We have shown that in order to find these correlation functions, one can perform averaging of some bilinear forms composed out of free Majorana fermions, and we presented the method for explicit calculation of these fermionic densities. We demonstrated how to derive an effective Hamiltonian for the Majorana fermions, including the effects of perturbations. For specific application of the general theory, we have studied the effect of the Dzyaloshinskii-Moriya (DM) anisotropic spin-spin interaction; we demonstrated that it leads, already in the second order over its relative magnitude D/K, to a power-law spin correlation functions, and calculated dynamical spin structure factor of the system. We have shown that an external magnetic field h in presence of the DM interaction, opens a gap in the excitation spectrum of magnitude proportional to Dh.

Kagome antiferromagnets display a host of exotic magnetic phenomena originating from a massive degeneracy of classical ground states. Presumably, this massive degeneracy is an accident and so the community's focus has been to discover ideal kagome antiferromagnets where it is present and study their properties. I will argue it is not an accident and that locality and, for example, a mirror symmetry are enough to guarantee frustration. In the process, I will uncover a rich theory of distorted kagome antiferromagnets, showing their ground states map onto triangulated surfaces with (origami) or without (kirigami) holes. I will show the exchange constants J_ij behave like a background gauge field whose geometry can determine some of the zero modes. From a different perspective, I will further show there are zero modes in the spin wave spectra determined by a topological classification of Maxwell counting by extending the 10-fold way classification of Hermitian matrices that underpin topological insulators to non-Hermitian matrices. I will conclude by applying the theory to two materials and demonstrate explicitly the existence of either flat bands (Cs_2ZrCu_3F_{12}) and line-degeneracies (Cs_2CeCu_3F_{12}) in the spin wave spectra and how this relates to the curvature and folding modes in the associated triangulated surface that characterize their ground states.

Formulating consistent theories describing strongly correlated metallic topological phases is an outstanding problem in condensed-matter physics. I will present an explicit construction of a fractionalized analog of the Weyl semimetal state: the fractional chiral metal. Our approach is to construct a 4+1D quantum Hall insulator by stacking 3+1D Weyl semimetals in a magnetic field. In a strong enough field, the low-energy physics is determined by the lowest Landau level of each Weyl semimetal, which is highly degenerate and chiral, motivating us to use a coupled-wire approach. In the presence of electron-electron interactions a gapped phase emerges; its electromagnetic response is given in terms of a Chern-Simons field theory. A boundary of this four dimensional phase remains gapless. The boundary's response to an external electromagnetic field is determined by a chiral anomaly with a fractional coefficient. We suggest that such an anomalous response can be taken as a working definition of a fractionalized strongly correlated analog of the Weyl semimetal state.

A major challenge in the study of strongly correlated electron systems is to establish a firm link between microscopic models and effective field theory. Quite often, this step involves a leap of faith, and/or extensive numerical studies. For fractional quantum Hall model wave functions, there exists - in some cases - a scheme to infer the long distance physics of the state that is both compelling and simple, and leaves very little room for ambiguity. This scheme involves a local parent Hamiltonian for the state, which unambiguously defines a "zero mode space" of elementary excitations, and what’s known as a "generalized Pauli principle", which efficiently organizes the zero mode space through one-dimensional patterns satisfying local rules. Where this works, universal properties of the state unambiguously emerge from counting exercises in terms of these patterns, which efficiently encode degeneracies, quasi-particle types and charges, and which completely determine an edge conformal field theory. There is even a natural scheme to infer braiding statistics directly, for both Abelian and non-Abelian states. Unfortunately, such a framework thus far exists for some quantum Hall states but not for others. In this talk, I will review the state of the art of this formalism, give reasons of why its "plain vanilla form" is insufficient to describe some important fractional quantum Hall states (e.g., Jain states), and explain how to address this deficiency through a new, more general concept, called "entangled Pauli principles". It will turn out that for some interesting quantum Hall states, the efficient description advertised here involves simple matrix-product-type entanglement. [1] arXiv:1803.00975

We study the temperature dependence of the electrical resistivity in a system composed of critical spin chains interacting with three dimensional conduction electrons and driven to criticality via an external magnetic field. The relevant experimental system is Yb2Pt2Pb, a metal where itinerant electrons coexist with localized moments of Yb-ions which can be described in terms of effective S=1/2 spins with dominantly one-dimensional exchange interaction. The spin subsystem becomes critical in a relatively weak magnetic field, where it behaves like a Luttinger liquid. We theoretically examine a Kondo lattice with different effective space dimensionalities of the two interacting subsystems. We characterize the corresponding non-Fermi liquid behavior due to the ``local criticality'' from the spins by calculating the electronic relaxation rate and the dc resistivity and establish its quasi linear temperature dependence.

We theoretically study an ultra-cold gas of spin-1 polar bosons in one spatial dimension which are subject to a quadratic Zeeman field and a Raman induced spin-orbit coupling. Concentrating on the regime in which the background fields can be treated perturbatively we analytically solve the model in its low-energy sector, i.e. we characterize the relevant phases and the quantum phase transitions between them. Depending on the sign of the effective quadratic Zeeman field epsilon, two superfluid phases with distinct nematic order appear. In addition, we uncover a spin-disordered superfluid phase at strong coupling. We employ a combination of renormalization group calculations and duality transformations to access the nature of the phase transitions. At epsilon=0, a line of spin-charge separated pairs of Luttinger liquids divides the two nematic phases and the transition to the spin disordered state at strong coupling is of the Berezinskii-Kosterlitz-Thouless type. In contrast, at epsilon not equal to 0, the quantum critical theory separating nematic and strong coupling spin disordered phases contains a Luttinger liquid in the charge sector that is coupled to a Majorana fermion in the spin sector (i.e. the critical theory at finite epsilon maps to a quantum critical Ising model that is coupled to the charge Luttinger liquid). Due to an emergent Lorentz symmetry, both have the same, logarithmically diverging velocity. We discuss the experimental signatures of our findings that are relevant to ongoing experiments in ultra-cold atomic gases of 23Na.

In recent years, a lot of effort has been devoted to the quest for experimental realizations of Kitaev interactions in spin systems. Recently, many materials have been proposed which seem to realize extended Kitaev models, where the Kitaev interactions are supplemented by Heisenberg and other bond dependent terms. The symmetry and electronic structure of these materials renders the determination of a minimal model a non trivial pursuit. In this talk I will concentrate on one of these particular materials, A-Li2IrO3, for which various minimal models have been proposed. Employing large scale Monte Carlo simulations I will show how the number of prospective models can be reduced. I will show that many of those models do not reproduce the most recent experimental results. Furthermore, I will propose and predict the results of an experiment which could help determine which one of the proposed models, if any, is the minimal model of A-Li2IrO3.

We develop a numerical technique based on the pseudofermion functional renormalization group (PFFRG) to calculate hopping and pairing amplitudes of emergent spinon quasiparticles in spin-1/2 quantum spin liquids. Within this approach, we first formulate a self-consistent Fock-like equation for these amplitudes where instead of the bare propagators and couplings we use the fully renormalized ones from PFFRG. We solve these equations using different ansätze for the hoppings and pairings which we take from a projective symmetry group (PSG) classification. From the overall size of these amplitudes we identify which of the PSGs are preferably realized in the system. We apply this approach to the antiferromagnetic J1-J2 Heisenberg model on the square lattice and to the antiferromagnetic nearest neighbor Heisenberg model on the kagome lattice. For the J1-J2 model, we find that in the regime of maximal frustration (J1~J2/2) the largest amplitudes are obtained for a U(1) pi-flux state with a Dirac cone spinon dispersion. In the case of the kagome model we identify a gapless Z2 pi-flux state where the bands show a Dirac-cone-like structure at finite energies but also feature a small circular Fermi surface at zero energy. We discuss our findings and benchmark them against variational Monte Carlo results.

Quantum field theories play an important role in many condensed matter systems for their description at low energies and long length scales. In 1+1 dimensional critical systems the energy spectrum and the spectrum of scaling dimensions are intimately related in the presence of conformal symmetry. In higher space-time dimensions this relation is more subtle and not well explored numerically. In this talk we motivate and review our recent effort to characterize 2+1 dimensional quantum field theories using computational techniques 2+targeting the energy spectrum on a spatial torus. We discuss several examples ranging from the O(N) Wilson Fisher theories and Gross-Neveu-Yukawa theories to deconfinement- confinement transitions in the context of topological ordered systems. We advocate a phenomenological picture that provides insight into the operator content of the critical field theories.

Topological superconductors hosting spatially well-separated Majorana bound states offer the possibility for realizing robust qubits protected from local environmental perturbations. Revealing new properties of Majorana bound states as well as establishing an experimentally feasible platform for Majorana-based quantum computing constitute two of the most urgent challenges in the field. In this talk, I will address these issues by discussing two setups of topological superconductors coupled to conventional superconductors: (1) The first setup comprises a Coulomb-blockaded time-reversal invariant topological superconductor island with Majorana Kramers pairs placed in an s-wave superconductor Josephson junction. I will discuss a 2Pi Josephson effect which is mediated by the Majorana Kramers pairs and whose direction is controlled by the joint parity of all four Majorana bound states on the island, a "Parity-controlled 2Pi Josephson effect". (2) The second setup constitutes a Majorana-based qubit in an all-superconducting circuit, a "Majorana Superconducting Qubit". I will demonstrate how universal quantum computation can be achieved in such a device and discuss advantages over conventional superconducting qubits. [1] C. Schrade and L. Fu, Parity-controlled 2Pi Josephson effect mediated by Majorana Kramers pairs, arXiv:1801.03511 [2] C. Schrade and L. Fu, Majorana Superconducting Qubit, arXiv:1803.01002

In this blackboard talk, I will first review the old results of Peschel en Emery, who devised a set of interacting spin-1/2 models, for which the degenerate ground states can be written in terms of product states. This model has more interesting properties, such as excited states that can be constructed explicitly, and one can find exact, local operators that swap the ground states. These results can be generalized to three state Clock models, and models with arbitrary spin. If time allows, I will comment on how to adapt the construction to arbitrary lattices.

Strong correlations between spin, charge and orbital degrees of freedom play an important role in materials and a recent development of ultrafast spectroscopies enabled to disentangle these relevant degrees of freedom by their temporal evolution. I will start with a summary of the charge carrier relaxation after the photo-excitation in Mott insulators described within the dynamical mean field theory (DMFT) and continue how this formalism can be extended to including the role of dynamical screening and non-local fluctuations (GW+EDFMT)[1,2]. Then I will open the question how to use the laser pulse to manipulate screening in Mott insulators. As an extreme example I will present a self-trapping of the system in the negative temperature state by a proper manipulation of the screening environment, which leads to the enhanced subgap response in the charge susceptibility. This population inversion leads to the low-energy anti-screening and I will comment on its experimental relevance. In the second part I will shed light on the role of spin fluctuations in the relaxation dynamics, which can be analysed by an extension of DMFT[3]. I will exemplify how optical pump probe techniques can be used to detect some basic theoretical ideas in higher dimensional doped antiferromagnets, like string states, Trugman paths and the lack of spin-charge separation. At the end I will provide an outlook how to extend these tools to an ab-initio description of strongly correlated materials out of equilibrium. [1] D. Golez, M. Eckstein, and P. Werner. Phys. Rev. B, 92:195123, Nov (2015). [2] D. Golez, L. Boehnke, H. U. R. Strand, M. Eckstein, and P. Werner. Phys. Rev. Lett. 118:246402 (2017). [3] N. Bittner, D. Golez, M. Eckstein, P. Werner, in preparation.

Exactly solvable nonlinear wave equations -- colloquially known as the soliton systems -- are widely regarded as one of the greatest achievements of mathematical physics. But somehow, aside of several mathematical frameworks and other formal aspects, not a lot seems to be known about statistical properties of classical integrable field theories and, in particular, classical transport properties at finite temperature. In this talk, we present a kinetic equation to deal with dense soliton gases, expressed in terms of a linear integral dressing equation for the soliton spectral function which accounts for renormalization of the soliton velocities due to the interactions with a soliton many-body state. This is accomplished in the framework of the algebro-geometric integration technique which permits to classify all quasi-periodic solutions of an integrable equation of motion in terms of the moduli of finite-genus Riemann surfaces. By identifying soliton excitations, applying Born-Sommerfeld quantization for soliton orbits, extracting the two-body S-matrix, and finally taking the thermodynamic finite-density, the free energy functional is expressed as the saddle point of the action-space path-integral. Our hydrodynamic equations can understood as the thermodynamic analogue of the celebrated Whitham's modulation equations. The equations are universal, and even apply to the quantum theories of solitons. If time permits, we show how to obtain a closed compact formula for the Drude weight in the quantum Heisenberg spin chain, and discuss peculiarities related to it.

Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. In this talk I will present how virtual symmetries in tensor networks, summarized by the framework of matrix product operator (MPO) injectivity, are substantial to the classification of not only bosonic but also fermionic topological order in two dimensional systems. I will briefly discuss how this fact relates to Levin-Wen string net models and Tuarev-Viro state sum constructions. For the sake of concreteness, two examples of fermionic topological order, the fermionic toric code and the Majorana dimer model, are discussed using the language of fermionic tensor networks.

A metal is a solid with a Fermi surface. It is known how to reconstruct the shape of the Fermi surface – by immersing the metal in a magnetic field and measuring the period of field-induced oscillations of the magnetization/resistivity. I will show how to extract information about the quantum-mechanical wavefunction of the Fermi surface – from measuring the phase offset of these same oscillations. In some metals, this information is robust against deformations of the Hamiltonian (describing the metal), and may therefore be viewed as a topological invariant.

The paradigmatic condensed-matter models where zero-energy localized Majorana fermions have been studied so far have the distinguishing feature of not conserving the number of fermions. Moreover, the accepted definition of "Majorana fermion" naturally belongs to this scenario. Is it possible to discuss Majorana fermions in "canonical" particle-conserving settings? In this seminar I will present several exact and numerical results on Majorana fermions in particle-conserving scenarios. I will start from the discussion of a model for bosons and fermions where, in a proper limit, the physics of the celebrated Kitaev's chain appears. I will continue by presenting exact results on Majorana fermions in ladder models where the two legs of the system can only exchange pair of particles. Finally, I will comment on the possibility of making experiments with Majorana fermions in particle-conserving settings using cold atoms.

One of the most interesting properties of topologically ordered models with long ranged entanglement, such as Kitaev's toric code, is that they have anyonic excitations. The properties of these anyons can be recovered from first principles using techniques from mathematical physics, making it possible to put conjectures about such systems in a precise mathematical language. After explaining the main ideas behind this construction, I will discuss recent results on the stability of the excitation structure and on applications to quantum information theory.

In this talk I will given an overview of pure state quantum statistical mechanics, which is a new way of understanding issues at the foundation of statistical mechanics and thermodynamics. In particular, I will explain recent developments concerning equilibration and thermalization in closed quantum many-body systems. We will see how equilibration and thermalization can be defined in unitarily evolving and finite dimensional quantum systems, under which conditions they can be proved to happen, and what we know about the apparent equilibrium states. I will further speak about general results on structural properties both short- and long-range interacting many-body systems, with a focus on the decay of correlations in their thermal states. Finally, I will provide a glimpse of ongoing work concerning the use of machine learning tools form many-body physics and point out opportunities for future work.

Driving systems out of equilibrium can provide new ways to control properties and extract new functions. Recent development of intense laser in a wide frequency range has led to intriguing observations such as light-induced superconductivity-like behaviors above the transition temperature [1], enhancement of the excitonic condensation [2] and high-harmonic generation in solid states [3]. Motivated by this intriguing situation, we have been developing nonequilibrium methods based on the dynamical mean-field theory (DMFT). Here we would like to present recent two applications of the nonequilibrium DMFT for the time-periodic steady states (Floquet DMFT). In the first part, we discuss the high-harmonic generation (HHG) in the Mott insulator under periodic AC driving [4]. We show that qualitative behavior of the HHG spectrum is different between weak and strong field regimes, which originates from qualitative difference in doublon/holon dynamics under the driving. We also discuss the similarity and the difference of the HHG intensity in the Mott insulator compared to that of semiconductors and disordered systems. In the second part, we discuss the effects of the parametric-phonon driving on conventional SC, which has been considered to enhance SC[5][6]. By studying transient dynamics and steady states, we demonstrate that even though the attractive interaction can be enhanced by the driving, SC is always suppressed, in particular, at the parametric resonance. Our systematic analysis shows that, in a wide parameter range, the heating of the system is the dominant effect and the parametric phonon driving has a negative effect on SC. [1] M. Mitrano et al., Nature 530, 461 (2016). [2] S. Mor et al., PRL 119, 086401 (2017). [3] S. Ghimire et al., Nat. Phys. 7, 138 (2011). [4] Y. Murakami, M. Eckstein, P. Werner to be published. [5] M. Knap et al., PRB 94, 214504 (2016); M. Babadi et al., PRB 96, 014512 (2017). [6] Y. Murakami et al, PRB 96, 045125 (2017).

Fracton phases are gapped quantum phases in three dimensions that go beyond the standard paradigm of topological order; they have fractionalized excitations that are immobile or only mobile along lower-dimensional subsystems, such as lines or planes. While there are several exactly solvable models of such fracton phases, these models are far from realistic because they involve interactions between many spins at the same time. By generalizing the fermionic parton construction, a standard phenomenological description of fractionalization in quantum phases, we provide simple variational states capturing fracton phases. Moreover, by showing that each variational state is the asymptotic strong-coupling ground state of a corresponding coupled-spin-chain model, we demonstrate that a large class of fracton phases can be realized in more realistic models involving only two-spin interactions.

Topological semimetals have recently been one of the most active topics in solid state physics, and provide an exceptionally fruitful meeting point for fields as diverse as chemistry, band structure calculations and high-energy field theory. This talk will discuss the observation of quantum anomalies in Weyl semimetals. These anomalies are rooted in an incompatibility of quantum mechanics and classical conservation laws. In particular, I will focus on recent measurements demonstrating the presence of the mixed axial-gravitational anomaly in Weyl semimetals. In contrast to earlier expectations, which would for example search for this phenomenon in the hydrodynamics of neutron stars, we used a conceptually simple thermoelectric transport experiment to find signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP.

Higher-order topological insulators have been recently proposed as unprecedented quantum states of matter. In two spatial dimensions, they incorporate quantized electric quadrupole insulators, which feature zero-dimensional topological corner midgap states. These states are protected by the bulk gap, reflection symmetries, and a spectral symmetry, while their edges are gapped. Although such novel topological phases are often hard to come by in real materials, there are various analogue platforms that enable us to realize the corresponding band theory concepts in classical systems. I will talk about how we developed and measured a topolectrical circuit design for a quadrupole insulator, the midgap states of which manifest themselves as topological boundary resonances in the corner impedance profile of the circuit. This establishes an instance where topolectrical circuitry is employed to bridge the gap between quantum theoretical modeling and the experimental realization of topological band structures.

The computational superiority of a computer that operates according to the laws of quantum mechanics relies crucially on quantum parallelism: different sets of data stored as a superposition of quantum states can be processed in parallel. To play out this advantage, however, one has to be able to prepare such superpositions in the first place --- using only a minimum of computational resources. We present a framework to efficiently prepare superpositions of many-body spin configurations with programmable squared amplitudes. The spin configurations are encoded in the degenerate ground states of the lattice-gauge representation of an all-to-all connected Ising spin glass. The ground state manifold is invariant under variations of the gauge degrees of freedom, which take the form of four-body parity constraints. Our framework makes use of these degrees of freedom by individually tuning them to dynamically prepare programmable superpositions. The dynamics combines an adiabatic protocol with controlled diabatic transitions.

We discuss the perturbative control of low-energy effective theory of strongly-interacting systems which cannot be treated within the Landau Fermi liquid framework. These are generically called non-Fermi liquids where quasiparticles do not exist. In particular, we focus on critical Fermi surface states where there is a well-defined Fermi surface, but no quasiparticle resulting from the strong interaction between the Fermi surface and a massless boson. We will show that for Fermi surface having a dimension m>1, the Fermi momentum k_F enters the expressions for physical quantities as a dimensionful parameter leading to UV/IR mixing, thus modifying the naive scaling arguments, whereas for a one-dimensional Fermi surface there is an emergent locality with no such k_F dependence.

Non-relativistic quantum matter, as realized in ultracold atomic gases, continues to be a remarkably versatile playground for many-body physics. Experimentalists have exquisite control over temperature, density, coupling, and shape of the trapping potential. Additionally, a wide range of properties can be measured: from simple ones like equations of state to more involved ones like the bulk viscosity and entanglement. The latter has received much attention due to its connection to quantum phase transitions, but it has proven extremely difficult to compute: stochastic methods display exponential signal-to-noise issues of a very similar nature as those due to the infamous sign problem affecting finite-density QCD. In this talk, I will present an algorithm that solves the signal-to-noise issue for entanglement, and I will show results for strongly interacting systems in three spatial dimensions that are the first of their kind. I will also present a few recent explorations of the thermodynamics of polarized matter and other cases that usually have a sign problem, using complexified stochastic quantization.

A promising approach to realize quantum spin liquids is to enhance the spin-space symmetry from usual SU(2) to SU(N). While the SU(N) symmetry with a general N is proposed in ultracold atoms using nuclear spin degrees of freedom, its realization in magnetic materials is challenging. Here we propose a new mechanism by which the SU(4) symmetry emerges in the strong spin-orbit coupling limit. The spin-orbit coupling in d^1 transition metal compounds with edge-sharing anion octahedra leads to strongly bond-dependent hopping, which is apparently not SU(4)-symmetric. However, in the honeycomb structure, a gauge transformation maps the system to an SU(4)-symmetric Hubbard model. In the strong repulsion limit at quarter filling, the low-energy effective model is the SU(4) Heisenberg model on the honeycomb lattice, which cannot have a trivial gapped ground state and is expected to host a gapless spin-orbital liquid. By generalizing this model to other three-dimensional lattices, we also propose crystalline spin-orbital liquids protected by this emergent SU(4) symmetry and space group symmetries.

In the first part of the talk, I will propose a transport experiment of excitons in 2d transition-metal dichalcogenides. Due to their interactions with unbound electrons in the Fermi sea, excitons are dressed by a cloud of particle-hole excitations forming Fermi polarons. An in-plane electric field cannot directly accelerate neutral excitons, however, due to the polaronic dressing, the unbound electrons will drag the excitons along. This phenomenon is similar to Coulomb drag in bilayer semiconductors. We determine the drag conductivity for a low density of excitons using simple arguments as well as a diagrammatic calculation based on a self-consistent T matrix approximation. Due to the strong nonperturbative coupling, the exciton drag mobility is expected to be of the same order as the electron mobility even at zero temperature. Time permitting, I will discuss a novel probe of quantum Hall ferromagnetism in graphene based on thermal transport in the second part of the talk. Strong interactions lift the high degeneracy of the zero-energy Landau level in graphene mono- and bilayers, giving rise to a rich phase diagram of competing spin and valley order. Here we show that thermal transport at low temperatures can give compelling evidence for spontaneous symmetry breaking and exhibits many other signatures distinguishing the various phases.

An interesting topic in the theory of quantum phase transitions is that of the transition between a classically ordered state, such as a Néel state, and a quantum ordered state, such as a valence bond crystal. On the classically ordered side of the transition, we have a well developed understanding based on the spontaneous breaking of a continuous symmetry and the occurrence of associated Goldstone modes (spin waves). On the quantum ordered side, things are rather less clear. Even the description of the quantum ordered state itself is not straightforward, since it is not a saddle-point of the usual spin-coherent-state path integral. In this talk, I shall present an approach designed to address this problem by constructing the path integral over matrix product states rather than spin coherent states. This allows both classically ordered states (which are matrix product states of bond dimension 1) and quantum ordered states (which are matrix product states of higher bond dimension) to be captured on an equal footing. I shall use this approach to show that, for at least one example of such a transition, a Landau-Ginzburg-Wilson-type description can be given, where the ‘order parameter’ is a field representing the nearest-neighbour entanglement of the spins. The talk is designed to be entirely self-contained: in particular, no prior knowledge of matrix product states or quantum ordered phases is assumed. The work about which I shall speak was undertaken in collaboration with Andrew Green (University College London), Jonathan Keeling (St Andrews), and Steve Simon (Oxford), under the auspices of the TOPNES programme. Most of the details can be found at https://arxiv.org/abs/1607.01778.

The study of topological phases of matter is among the most active research fields in modern solid state physics. Over the last couple of years, there has been growing interest in the topological classification of gapless systems. One example of a gapless system, with defining topological properties, is the Weyl semimetal (TWS). In Weyl semimetals, conduction and valence bands touch at isolated points in the Brillouin zone. These Weyl points are topologically pro- tected and can only disappear if they annihilate pairwise. The Weyl semimetal hosts non-trivial surface states, which take the form of open Fermi arcs, connect- ing the projections of two Weyl points to the Brillouin zone of the surface. Due to the robustness of this phase, Weyl semimetals are of interest for applications in quantum computers or electronic devices. In this work, we consider a model for the iridium electrons in pyrochlore iridates. For this material class, a Weyl- semimetal phase has been predicted. We calculate the phase diagram and find a rich variety of phases, the TWS, a strong topological insulator, a type-II Weyl semimetal and various kinds of magnetic order. For the TWS, we study the un- conventional surface states for various geometries. For lower electron densities, we find a plethora of new magnetic configurations. We then turn our attention towards possible instabilities in Weyl semimetals. We study the stability of the Weyl semimetal phase against the formation of charge density waves. In the back- folded Brillouin zone, Weyl points that were originally far apart can be mapped close to each other and annihilate if that reduces the free energy. However we did not find a charge density wave. We therefore study the behavior of Weyl points under the influence of a charge density wave. We find mechanisms, that could possibly avoid the formation of such a charge configuration. For example, one-dimensional Fermi lines emerge.

Experimentalists have recently been able to engineer non-trivial topological band structures using ultracold atoms in optical lattices. Motivated by ongoing experimental efforts to tune interactions, we explore the interplay between strong correlations and topology in these systems. Focusing on the Haldane-Hubbard honeycomb model as an example, we show that its strongly interacting Mott limit exhibits various chiral magnetic orders, including a wide regime of triple-Q tetrahedral order. Incorporating an additional third-neighbour hopping frustrates and ultimately melts the tetrahedral magnetic order. From analysing low energy spectra, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid with gapped semion excitations. Our numerical results suggest that this frustration induced melting may be realised as an exotic continuous quantum phase transition. Finally, we discuss recent results which point toward a common mechanism of realising chiral spin liquids in Mott insulators through the continuous melting of non-coplanar magnetic "parent" states.

It has been known that the topological entanglement entropy is a useful order parameter to detect topologically ordered phases. When global symmetries are imposed, new types of topological phases emerge. They are called symmetry protected topological (SPT) phases for short range entangled states and symmetry enriched topological (SET) phases for long range entangled states. Since the entanglement entropy is insensitive to global symmetries, the topological entanglement entropy is no longer a good order parameter to distinguish SPT and SET phases. In this talk I introduce a new entanglement quantity, a charged entanglement entropy, by grand canonically generalising the entanglement entropy. This charged entanglement entropy is sensitive to global symmetries, and it shows a new universal term, in addition to the topological entanglement entropy, which can be used to distinguish SPT and SET phases.

We investigate the effects of Dzyaloshinsky-Moriya (DM) interactions on the frustrated J_1-J_2 kagome-Heisenberg model using the pseudo-fermion functional-renormalization-group (PFFRG) technique. In order to treat the off-diagonal nature of DM interactions, we develop an extended PFFRG scheme. We benchmark this approach in parameter regimes that have previously been studied with other methods and find good agreement of the magnetic phase diagram. Particularly, finite DM interactions are found to stabilize all types of non-collinear magnetic orders of the J_1-J_2 Heisenberg model (q=0, √3x√3, and cuboc orders) and shrink the extents of magnetically disordered phases. We discuss our results in the light of the mineral herbertsmithite which has been experimentally predicted to host a quantum spin liquid at low temperatures. Our PFFRG data indicates that this material lies in close proximity to a quantum critical point. In parts of the experimentally relevant parameter regime for herbertsmithite, the spin-correlation profile is found to be in good qualitative agreement with recent inelastic-neutron-scattering data.

In a celebrated recent result, Fawzi and Renner [CMP 340 (2015)] showed that for a given quantum state, and a tripatition ABC of a quantum system, the conditional mutual information I(A:C|B) is small if and only if there exists a map which approximately recovers the erasure of subsystem C, without acting on system A. Such states are called Markov states, and the maps are called local recovery maps. I will consider applications of this important new result to the analysis of many-body systems. In particular, I will show that if the thermal (Gibbs) state of a local Hamiltonian is Markov, and satisfies some physically reasonable assumption on the long range correlations, then (i) expectation values of local observables can be evaluated efficiently, and (ii) the Gibbs state can be sampled (prepared) efficiently on a quantum computer. Using similar methods, I will argue that ground states of certain local gapped Hamiltonians can be prepared in sub-linear time (on a quantum computer) if and only if the topological entanglement entropy is zero. Furthermore, a slight strengthening of these methods provide checkable conditions for the parent Hamiltonian of a PEPS to be gapped, as long as the Li-Haldane type conjecture holds. I'll finally comment on further applications of local recovery maps, including approximate error correcting codes and toy models for the AdS/CFT correspondence, and argue that these tools from quantum information theory will play an important role in analysis of many body systems.

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the first experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which have a direct and efficient implementation on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulating high-energy theories with atomic physics experiments, the long-term vision being the extension to real-time quantum simulations of non-Abelian lattice gauge theories. [1] E. A. Martinez*, C. A. Muschik*, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zoller, and R. Blatt, Nature 534, 516-519 (2016).

A major challenge in next-generation magnetic storage technologies is the efficient and controllable creation and manipulation of magnetic textures. We predict a way to create magnetic domain walls and skyrmions by means of a homogeneous DC current without the need of specialized setups and without requiring any standard “twisting” interactions like Dzyaloshinskii-Moriya or dipole-dipole interactions. This is possible by exploiting a dynamical instability arising by the interplay of current-induced spin-transfer torque and locally engineered anisotropies. The magnetic textures can be created efficiently, controllably and periodically with a period that can be tuned by the applied current strength. We propose specific experimental setups to observe the periodic formation of domain walls and skyrmions.

We investigate the quantum phases of the frustrated spin-$\frac{1}{2}$ $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice with ferromagnetic $J_1$ and antiferromagnetic $J_2$ and $J_3$ interactions. Using the pseudo-fermion functional renormalization group technique, we find an intermediate paramagnetic phase located between classically ordered ferromagnetic, stripy antiferromagnetic, and incommensurate spiral phases. We observe that quantum fluctuations lead to significant shifts of the spiral pitch angles compared to the classical limit. By computing the response of the system with respect to various spin rotation and lattice symmetry-breaking perturbations, we identify a complex interplay between different nematic spin states in the paramagnetic phase. While retaining time-reversal invariance, these phases either break spin-rotation symmetry, lattice-rotation symmetry, or a combination of both. We therefore propose the $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice as a paradigmatic example where different intimately connected types of nematicities emerge in the same model.

Results are presented from large-scale quantum Monte Carlo simulations on the excitation modes in two- and three-dimensional quantum antiferromagnets of coupled spin dimers accross their quantum critical points. The identification of the amplitude (Higgs) mode from dynamical spin and singlet spectral functions are examined and compared to scaling predictions. For the three-dimensional case, we identify characteristic multiplicative logarithmic corrections in the exciation gap scaling atop the leading mean-field behavior. These are in accord with field-theoretical predictions based on an effective description of the quantum critical system in terms of an asymptotically-free field theory. The width of the Higgs mode resonance is observed to scale linearly with the Higgs mass near criticality, indicative of this critically well-defined excitation mode of the symmetry broken phase.

Manipulation of spin textures has been attracting a broad interest from the viewpoints of both fundamental physics and applications over decades. In particular, the control magnetic skyrmions is one of the hottest topics. In the first part of my talk, I will talk about the static deformation of skyrmion crystals under uniaxial strain revealed by the Lorentz TEM observation. This experimental result is analyzed by the model with an anisotropic Dzyaloshinskii-Moriya interaction, which shows a good agreement with the experiment. In the next part, I will discuss the dynamical deformation of skyrmion crystals under a driving current and the corresponding suppression of the Bragg peak intensities, which we expect to be measured by neutron scattering experiments.

Quantum spin liquids are fascinating phases in quantum magnetism. Broad theoretical advances, and fast progress in materials science have significantly advanced the field in recent years. After a general introduction to the subject, I will talk about the projective symmetry group approach to the problem of classification of such exotic phases. In a second part, I will present work on the theory for the kapellasite material, a spin S=1/2 Heisenberg antiferromagnet on the kagome lattice. Finally, I will discuss a highly intriguing phase that was recently characterized in the triangular spin S=1 compound BaNiSbO. SB et al, PRB 93, 094437 (2016). SB et al, PRB 92, 060407(R) (2015). B. Fak, SB, et al, arXiv:1610.03753 (2016).

Thanks to the recent impressing experimental progresses the investigation of non- equilibrium properties of driven-dissipative systems has entered the quantum world. Rydberg atoms in optical lattices, systems of trapped ions, exciton- polariton condensates, cold atoms in cavities, arrays of coupled QED cavities, are probably the most intensively investigated experimental platforms in relation to this aim. I will discuss properties of phases and phase transitions in the steady state of these systems.

Light can be converted into a liquid, a quantum liquid called Bose-Einstein condensate, where it nearly stops if travels in one dimension. In this talk, I address a quasiequilibrium one-dimensional Bose-Einstein condensation of photons trapped in a microtube, which is possible because the light modes have a cut-off frequency (a photon’s “mass”) and interact through different processes of absorption, emission, and scattering on molecules and atoms. I discuss the conditions for the one-dimensional condensation of light and the role of photon- photon interactions in the system. This theoretical study is in the strong connection with the experiments of the Weitz Quantum Optics group (University of Bonn).

Tensor networks provide a novel and powerful way to think about and perform calculations with many-body systems. This talk treats tensor networks in the form of Matrix Product states (MPS) and Matrix Product Operators (MPO), which are used for calculations on (1D) spin chains. Firstly, Density Matrix Renormalization Group (DMRG) algorithms, concerned with finding the ground state and its energy. Secondly, an approach for the minimization of entanglement entropy using unitary basis transformations is given. The idea for this latter part is based on [1], but instead of a parameter-based approach, an environment network-based algorithm is used. The combination of the entropy minimization with DMRG is discussed. Results obtained using the minimization algorithm are shown, and the method's limitations are discussed. [1] C. Krumnow, L. Veis, Ö. Legeza & J. Eisert, Fermionic orbital optimisation in tensor network states, arXiv 1504.00042v3

We report the results of the full parquet renormalization group (pRG) analysis of the 5-pocket model for Fe-based superconductors (three hole pockets and two electron pockets). We depart from the low-energy orbital model and use as input the fact that excitations near all five pockets are made out of xz, yz, and xy d-orbitals. We argue, based on symmetry that there are 40 different coupling constants which describe the interactions between low-energy fermions and flow under pRG. The pRG analysis reveals four stable fixed trajectories. They can be grouped into two classes, where the 5-pocket model effectively reduces either to a 3-pocket or a 4-pocket one. We argue that in both cases superconductivity wins over SDW if all five Fermi energies are small and pRG runs over a wide energy range. The resulting superconducting symmetry is ! of s+- fo r m for both effective models, but the magnitude of the gap differs between the hole pockets at (0,0) and (pi,pi) in the 1Fe zone. SDW magnetism is of stripe type in the 3-pocket and of checkerboard type in the 4-pocket case. Additionally a spontaneous orbital order develops before superconductivity that splits the band degeneracy at high-symmetry points.

Quantum systems in contact with an environment display a rich physics emerging from the interplay between dissipative and Hamiltonian terms. We consider a dissipative boundary driven ladder in presence of a gauge field. The dissipation stimulates currents while the gauge field tends to steer the flow. We show that depending on the geometry of coupling to the baths and of the strength of the gauge field, non-equilibrium phase transitions emerge strongly modifying the currents both in magnitude and spatial distribution.

In recent years, many-body localization and the prediction of a metal-insulator transition at finite temperature has attracted a lot of attention as a way to maintain permanent off-equilibrium conditions in a thermodynamic, but closed quantum many-body system. Such transitions, driven by energy density (or ”temperature”), require the presence of a many-body mobility edge in energy, that separates localized from ergodic states. I argue that for short range interactions this scenario is beyond the control of perturbation theory and seems inconsistent due to inclusions of the ergodic phase in the supposedly localized phase. Those inclusions are mobile and induce global delocalization. These considerations modify the phase diagrams for interacting systems both with and without quenched disorder.

Due to experimental advances in the preparation and control of ultra-cold atomic gases, there is a widespread interest in the behaviour of quantum systems out of equilibrium. A common way to probe quantum systems for non-equilibrium phenomena is given by sudden quenches. I will present results concerning the dynamics of the longitudinal spin correlation function after a sudden quench in the Transverse Field Ising Chain. A distinguishing feature of this model is that it exhibits a quantum critical point separating a ferromagnetic from a paramagnetic phase. Furthermore, the system can be expressed as a fermionic harmonic oscillator, which allows us to determine the longitudinal correlation function after a sudden quench exactly by using Wick's theorem. In particular, I will concentrate on the behaviour of the longitudinal correlation function for quenches from an initially large external field to the vicinity of the quantum critical point within the paramagnetic phase. We conjectured a formula for the asymptotic behaviour in this case and compared it to numerical calculations of the correlator. Based on this conjectured formula, we found that the decay of the correlation function is characterized by two correlation lengths and that the correlation function attains its stationary values already at short distances.

I will introduce some basic facts about the AdS/CFT correspondance which may be relevant to tensor network models. The group of isometries of Anti de Sitter space is also the group of Lorentzian conformal maps on its "boundary at infinity". Similarly, the isometries of Hyperbolic space or de Sitter space form the Euclidean conformal group. Thinking of path integrals as continuous tensor networks, one can see how the ground state of a quantum field theory in AdS space may be thought of as that of a conformal field theory on its boundary, whose correlators are represented by tree tensor networks. TTNs also arise when computing correlators in MERA, which can be thought of as a discretisation of de Sitter space. Is there a formal relationship between these two pictures?

In this seminar, I will discuss how complementing the Bose-Hubbard model with soft-shoulder interactions allows for the stabilization of exotic state of matters which, in one- and two-dimensions, break the typical Luttinger and Landau liquid paradigms. In the first part talk, I will present discuss the basic classical statistical mechanics ingredients of such potentials, which support cluster solutions with extensive ground state degeneracy. Using a combination of field theoretical and numerical approaches, the phase diagram of the model will be presented. In particular, I will focus on the existence of a Cluster Luttinger liquid phase, which cannot be captured using conventional ‘coarse graining’ schemes of Abelian bosonization, and show how this phase is separated by a conventional Luttinger liquid via a phase transition with emergent conformal supersymmetry. In the second part of the talk, I will discuss the fate of such states and transitions in two-dimensions using numerical simulations. In this context, strong soft-shoulder interactions lead to a dramatic change of the ‘Bose surface’, and stabilize a phase with no broken symmetry but still displaying quasi-long-range coherence, of Bose-metal type. The mechanism for the stabilization of such exotic liquids is clusterization, which defines a low-energy manifold displaying extensive ground state degeneracy and, and the same time, suppress superfluid order. Finally, I will present some considerations on the experimental realization of both one- and two-dimensional cases using laser-dressed Rydberg atoms.

In the first part of the talk, the recent advance in the theory of the anomalous Hall effect is reviewed. Remarkably, it was shown that diagrams with crossed impurity lines yield an anomalous Hall conductivity that is independent of impurity concentration, and thus is of the same order as other known extrinsic side jump and skew scattering terms. Based on a semiclassical interpretation, we explain that such diagrams represent diffractive skew scattering contributions originating from rare two-impurity complexes. Next, results for the anomalous Hall conductivity sigma_xy of the surface states in cubic topological Kondo insulators are presented. We consider a generic model for the surface states with three Dirac cones on the (001) surface: The Fermi velocity, the Fermi momentum and the Zeeman energy in different Dirac pockets may be unequal. The microscopic impurity potential mediates mixed intra and interband extrinsic scattering processes. We discuss various special cases of our results and the experimental relevance of our study in the context of the recent hysteretic magnetotransport data in SmB6 samples. The last part of the talk is devoted to our recent study of the temperature dependent anomalous ac Hall conductance sigma_xy(omega, T) for a 2D chiral p-wave superconductor [3]. This quantity determines the polar Kerr effect, as it was observed in Sr2RuO4. We concentrate on a single band model with generic, isotropic dispersion relation subjected to rare, weak impurities treated in the Born approximation. Again, the emphasis is on diffractive skew scattering from quantum impurity complexes. It is explicitly shown, that this effect contributes to leading order in impurity concentration and is thus comparable to earlier results within the same model.

In my talk I will start with a review of our recent work on realizing a broad class of lattice spin-1/2 models with cold alkali atoms stored in optical or magnetic trap arrays. In particular, we exploit the strong angular dependence of van der Waals interactions between high angular momentum Rydberg states. Together with the possibility of designing step-like potentials we can implement Abelian gauge theories in a series of geometries, which could be demonstrated within state of the art experiments. The resulting energy scales of interactions compare well with typical temperatures and decoherence time-scales, making the exploration of exotic forms of quantum magnetism, including emergent gauge theories, compass models and quantum spin ice models, accessible within state-of-the-art experiments.

In my talk I will introduce the spin liquid phases that occur in kagome antiferromagnets, and discuss their physical origin that are closely related with the newly discovered symmetry protected topological phase (SPT). I will first present our numerical (DMRG) study on the kagome XXZ spin model that exhibits two distinct spin liquid phases, namely the chiral spin liquid and the kagome spin liquid (the groundstate of the nearest neighbor kagome Heisenberg model). Both phases extend from the extreme easy-axis limit, through SU(2) symmetric point, to the pure easy-plane limit. The two phases are separated by a continuous phase transition. Motivated by these numerical results, I will then focus on the easy-axis kagome spin system, and reformulate it as a lattice gauge model. Such formulation enables us to achieve a controlled theoretical description for the spin liquid phases. We then show that the chiral spin liquid is indeed a gauged U(1) SPT phase. On the other hand, we also propose that the kagome spin liquid is a critical spin liquid phase, which can be considered as a gauged deconfined critical point between a SPT and a superfluid phase.

The fractional quantum Hall effect, which can be realized in certain two-dimensional systems at low temperature and high magnetic field, leads to many interesting properties, such as the possibility to have anyonic quasiparticles that are neither bosons nor fermions. There is currently much interest in investigating the possibilities for having fractional quantum Hall physics in lattice systems, both because it may lead to new ways to realize the effect, and because the lattice gives rise to new features and opportunities. Here, we propose a quite general approach based on conformal field theory to obtain lattice fractional quantum Hall models. The models have analytical ground states, and we use Monte Carlo simulations to compute, e.g., topological entanglement entropies and shape and statistics of anyons. We also discuss how one can interpolate between lattice and continuum fractional quantum Hall models and propose a scheme to implement a related model in ultracold atoms in optical lattices.

The phase diagram of quantum electrodynamics in three space-time dimensions as a function of fermion flavor number N exhibits two well-known phases: at large N > Nc1 the system is in a conformal gapless state, while for small N < Nc2 the fermions are expected to develop a dynamical mass due to spontaneous chiral symmetry breaking. Using epsilon expansion near the lower critical dimension of two, in combination with the recent results on the generalization of the F theorem to continuous dimension, we show that Nc1 > Nc2. There is therefore an intermediate range of values of N at which a third phase is stabilized. We demonstrate that this phase is characterized by spontaneous breaking of Lorentz symmetry, in which a composite vector boson field acquires a vacuum expectation value with the fermions and the photon remaining massless.

We propose an interacting many-body space-time-discrete Markov chain model, which is composed of an integrable deterministic and reversible cellular automaton (the rule 54 of [Bobenko et al, CMP 158, 127 (1993)]) on a finite one-dimensional lattice, and local stochastic Markov chains at the two lattice boundaries which provide chemical baths for absorbing or emitting the solitons. Ergodicity and mixing of this many-body Markov chain is proven for generic values of bath parameters, implying existence of a unique non-equilibrium steady state. The latter is constructed exactly and explicitly in terms of a particularly simple form of matrix product ansatz which is termed a patch ansatz. This gives rise to an explicit computation of observables and k-point correlations in the steady state as well as the construction of a nontrivial set of local conservation laws. Feasibility of an exact solution for the full spectrum and eigenvectors (decay modes) of the Markov matrix is suggested as well. We conjecture that such ideas can pave the road towards a theory of integrability of boundary driven classical deterministic lattice systems.

Quantum gases of interacting fermionic atoms in optical lattices promise to shed new light on the low-temperature phases of Hubbard-type models, such as Mott-insulating and spin-ordered phases or possible d-wave superconductivity. We experimentally realize the two-dimensional Hubbard model by loading a quantum degenerate two-component Fermi gas of 40K atoms into an anisotropic optical lattice geometry. Using high-resolution absorption imaging combined with radio-frequency spectroscopy we are able to resolve the in-situ distribution of singly and doubly occupied lattice sites within a single two-dimensional layer. In this talk, I will report on the in-situ observation of the fermionic Mott insulator and a measurement of the equation of state of the repulsive Hubbard model in two dimensions which constitutes a benchmark for state-of-the-art theoretical approaches.

Motivated by the entanglement properties of low-energy states of local Hamiltonians I introduce matrix product states (MPS) as a variational ansatz for the study of one dimensional quantum many-body systems. Then I apply the MPS formalism to study 1+1 dimensional QED, also know as the massive Schwinger model. I explain how MPS are used to compute an approximation of the ground state and discuss its entanglement properties. Next, MPS are used to study non-equilibrium dynamics by a quench in the form of a uniform background electric field. When the electric background field is small, the results are explained by investigating the low-energy spectrum of the Hamiltonian. For larger values of the quench we observe thermalisation. Finally, I discuss how the MPS framework is generalised to higher dimensions and can be used to simulate real-time evolution.

Tensor networks provide a natural framework for studying bulk-to-boundary or holographic correspondences. In this talk, we will explore the holographic properties of random tensor networks with large bond dimensions. We find that they realize many of the interesting structural features of the AdS/CFT correspondence in quantum gravity: Entanglement entropies of boundary subsystem correspond to minimal domain walls in the bulk, and the physics in the domain is encoded faithfully in the boundary subsystem. Increasing the entanglement in the bulk ultimately creates the analog of a black hole, with an associated Hawking-Page phase transition. All this can be understood by mapping the statistical properties of random tensors to the partition function of classical ferromagnetic Ising models. From the perspective of quantum information theory, random tensor networks implement quantum error-correcting codes with interesting locality properties, and their emergence can be understood as an assisted form of entanglement distillation.

Anomalous Hall effect arises in systems with both spin-orbit coupling and magnetization. Generally, there are three mechanisms contributing to anomalous Hall conductivity: intrinsic, side jump, and skew scattering. The standard diagrammatic approach to the anomalous Hall effect is limited to computation of ladder diagrams. We demonstrate that this approach is insufficient. An important additional contribution comes from diagrams with a single pair of intersecting disorder lines. This contribution constitutes an inherent part of skew scattering on pairs of closely located defects and essentially modifies previously obtained results for anomalous Hall conductivity. We argue that this statement is general and applies to all models of anomalous Hall effect. We illustrate it by an explicit calculation for two-dimensional massive Dirac fermions and for the Rashba ferromagnet model with weak disorder. In the case of Dirac electrons, inclusion of the diagrams with crossed impurity lines reverses the sign of the skew scattering term and strongly suppresses the total Hall conductivity at high electron concentrations. In the 2D Rashba model, the proposed mechanism provides the only contribution to the anomalous Hall conductivity in the most relevant metallic regime.

Recent experimental developments offer platforms to investigate the interaction between light and matter at the quantum level, encouraging the buildup of theoretical tools to describe their dynamics. The great control over the system parameters also permits to tune many-body Hamiltonians, opening the way to explore novel quantum phases. In this talk, I will first introduce a nano-engine device composed of a quantum dot coupled to external environments, and show that vacuum symmetry breaking generates a rectified current flowing through the device. I will then present a stochastic approach which aims at computing the out-of-equilibrium dynamics of spin-boson models. This approach permits to explore the strong coupling regime of the Rabi model, which is the simplest model of interaction between light and matter, and to investigate the quantum phase transition in the ohmic spinboson model, which describes a two-level system interacting with a dissipative environment. I will also present an hybrid setup comprising a double quantum dot coupled to a microwave cavity, which was realized recently. This system produces a highly entangled state of light and matter in relation to Kondo physics.

The local spectra of quantum states in SLOCC classes of n qubit states give rise to polytopes in n-dimensional real space. While for more than three qubits there are infinitely SLOCC classes, there are always finitely many so-called entanglement polytopes. The entanglement polytopes can be computed from a generating set of all covariants with respect to the group of local transformations. Furthermore, a duality between entanglement polytopes and algebraic varieties yields a description of different types of entanglement. In the talk, we will illustrate this approach and present results for entanglement polytopes for some five qubit states.

Trapped ions provide flexible emulators of spin Hamiltonians. In this talk, I will motivate to use ions for an implementation of a Mattis-type spin glass model. Finding the ground state of this model is equivalent to the optimization process in the number partitioning problem - a potentially NP-hard computational task. A transverse magnetic field introduces quantum effects, and opens the door to quantum annealing. A numerical study of the system dynamics demonstrates the feasibility of this approach.

Research in out-of-equilibrium quantum physics has recently revealed relaxation towards a non-thermal statistical ensemble (Generalised Gibbs Ensemble or shortly GGE) that retains more memory of the initial state than the conventional thermal ensemble. The information content of this ensemble remains however a riddle. By analytically studying the time evolution after abrupt changes (quantum quenches) in extended one-dimensional quantum systems, we demonstrate relaxation according to the GGE in various different settings and specify the information that survives in the stationary state. In the case of evolution under a gapless non-interacting Hamiltonian on the other hand, we observe the failure of the GGE and find evidence of a novel type of equilibration characterised by the preservation of non-Gaussian correlations of the initial state. We propose an experimental check of our predictions based on current experimental techniques.

Although light is the main tool in quantum gas physics, its quantumness is often neglected. We show that elevating light to a quantum variable leads to a plethora of novel many-body phenomena, unobtainable in classical optical setups. First, we prove that the quantum backaction of a weak global measurement can efficiently compete with standard short-range processes in a strongly correlated system (ultracold bosons or fermions in an optical lattice), leading to novel phenomena. We demonstrate generation of the multimode generalizations of Schroedinger cat and NOON states, nonlocal quantum Zeno dynamics, and non-Hermitian processes without the need of postselection. For fermions, we show the measurement-induced antiferromagnetic states, as well as the protection and break-up of strongly interacting fermion pairs. The backaction results in the generation of genuinely multipartite entangled modes of matter waves, which show non-Gaussian properties beyond quantum optical analogues. Second, trapping quantum gases inside a high-Q cavity, creates a paradigm of quantum optical lattices. We demonstrate the emergence of novel many-body phases: delocalized dimers, trimers, etc. of matter waves, even beyond the density orders such as density waves and supersolids. We show that cavity QED of strongly correlated systems can efficiently simulate systems with short- and long-range interactions, while still profiting from the collective enhancement of the light-matter interaction.

We elaborate on a proposal for the state preparation of quantum many-body systems by engineered dissipation. Specifically, we discuss the purely dissipative dynamics of a large system of s = 1/2 quantum spins or, equivalently, hard-core bosons on a regular lattice. In the first part of the talk, we introduce the underlying quantum master equation (Lindblad equation) and exemplify how it can be used to determine the equations of motion for correlation functions. In the second part of the talk, we resolve the real-time dynamics of the dissipative process. This allows us to identify different characteristic time scales for the dynamics for which we determine their finite-size scaling. We introduce the concept of cumulative entanglement distribution to quantify multi-particle entanglement and show that the considered protocol serves as an efficient method to prepare a macroscopically entangled Bose-Einstein condensate.

The ergodic hypothesis for an isolated quantum system has been a subject of intense investigation in recent years. Under what conditions does a quantum system thermalize in the absence of a heat bath? It has been argued that in the presence of strong disorder, a system loses its ability to equilibrate itself even at infinite temperature, a phenomena now known as many-body localization (MBL). I will review the basic notions of this new phase of matter characterized by its dynamics. Due to the violation of equilibrium statistical physics in this phase, MBL protects topological and symmetry-breaking orders in situations where they are destroyed at thermal equilibrium. In this talk I will discuss the phase transition between MBL and ergodic phases tuned by energy density, leading to a finite temperature mobility edge. As concrete examples I will focus on the one-dimensional random-field Heisenberg and the infinite-dimensional quantum random energy models. The latter has been a useful mean-field model for analyzing the thermodynamic spin-glass transition. Its tractability allows the comparison between analytical and numerical study of a finite temperature mobility edge.

I discuss the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the two ordered phases meet. With the functional renormalization group approach, we reveal a complex structure of fixed points. Their the stability properties decisively depend on the number of Dirac fermions Nf. We give estimates for the critical exponents and observe crucial quantitative corrections as compared to a previous first-order epsilon expansion. For small Nf, the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large Nf, a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate Nf, including the graphene case (Nf=2) no stable and physically admissible fixed point exists. We therefore suggest that Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic and staggered density phases is governed by a triple point exhibiting first-order transitions.

The problem of a quantum Ising degree of freedom coupled to a gapless bosonic mode appears naturally in many one dimensional systems, yet surprisingly little is known how such a coupling affects the Ising quantum critical point. We investigate the fate of the critical point in a regime, where the weak coupling RG indicates a flow toward strong coupling. Using renormalization group analysis and numerical density matrix renormalization group (DMRG) calculations we show that quantum fluctuations near the critical point cause phase separation on an emergent long scale, and the transition becomes first order. This suggests the existence of a tricritical point with potentially exotic properties.

Braiding of Majorana zero modes provides a promising platform for quantum information processing. Strictly speaking, however, the scheme relies on infinite braiding times as it utilizes the adiabatic limit. I will discuss how to minimize nonadiabatic errors for finite braiding times by finding an optimal protocol for the Majorana movement or adding so-called counter-diabatic terms to the Hamiltonian. In the second part of the talk I will present a scheme to substantially increase the robustness of a Majorana pi/8 phase gate, which is a missing ingredient when implementing universal quantum computation using Majorana bound states.

In certain Sm systems with mixed valence such as SmOs4Sb12 and SmT2Al20 with T=Ti, V, Cr, Ta, etc, the resistivity and specific heat show behaviors reminiscent of the Kondo effect. However, the behaviors are almost independent of applied magnetic field. We ascribe the Kondo-like behavior to charge correlations. Acccoding to our model, the effective hybridization of Sm 4f-electrons is reduced by the orthogonality effect with the Coulomb interaction U between 4f and conduction electrons. The Coulomb interaction also acts to enhance the hybridization via the exciton-like correlation. The orthogonality effect becomes dominant as U and/or the number of conduction channels increases, and eventually makes the effective hybridization vanish. We combine the continuous-time Monte Carlo calculation and the analytic theory to derive the dynamics in the wide temperature range.

Magnetic skyrmions have the potential to provide solutions for low-power, high-density data storage and processing. One of the major challenges in developing skyrmion-based devices is the skyrmions' magnetic stability in confined helimagnetic nanostructures. Through a systematic study of equilibrium states, using a full three-dimensional micromagnetic model including demagnetisation effects, we demonstrate that skyrmionic textures are the lowest energy states in helimagnetic thin film nanostructures at zero external magnetic field and in absence of magnetocrystalline anisotropy. We also report the regions of metastability for non-ground state equilibrium configurations. We show that bistable skyrmionic textures undergo hysteretic behaviour between two energetically equivalent skyrmionic states with different core orientation, even in absence of both magnetocrystalline and demagnetisation-based shape anisotropies, suggesting the existence of novel Dzyaloshinskii-Moriya-based shape anisotropy. We also show that the skyrmionic texture core reversal dynamics is facilitated by the Bloch point occurrence and propagation. Finally, we report the resonance frequencies and corresponding normal modes of all identified equilibrium states as well as how the resonance frequencies change depending on both the external magnetic bias field and disk sample diameter.

We identify a new universality class in one-dimensional driven open quantum systems with a dark state. Salient features are the persistence of both the microscopic non-equilibrium conditions as well as the quantum coherence of dynamics close to criticality. This provides a non-equilibrium analogue of quantum criticality, and is sharply distinct from more generic driven systems, where both effective thermalization as well as asymptotic decoherence ensue, paralleling classical dynamical criticality. We quantify universality by computing the full set of independent critical exponents within a functional renormalization group approach.

The investigation of spin liquids is a fascinating field in condensed matter physics that is increasingly motivated by experiments. Exhaustive classifications of spin liquids have been carried out in several systems, particularly when full SU(2) spin-rotation symmetry is present. Systematic studies that explore strongly spin-orbit-coupled magnetic compounds (for which there are many experimental examples) are, however, relatively scarce. We report on a classification of Z_2 spin liquids on the square lattice when SU(2) spin symmetry is maximally lifted. Using projective symmetry group methods, we find that, surprisingly, the lifting of spin symmetry yields vastly more spin liquid states compared to SU(2)-invariant systems. A generic feature of the SU(2)-broken case is that the spinons naturally undergo p+ip pairing; consequently, many of these Z_2 spin liquids feature a topologically nontrivial spinon band structure supporting gapless Majorana edge states. These boundary modes are often protected by a combination of time reversal and lattice symmetries and hence resemble recently proposed topological crystalline superconductors.

Manipulating small spin textures, which can serve as bits of information, by electric current is one of the main challenges in the field of spintronics. Ferromagnetic skyrmions recently attracted a lot of attention because they are small in size and are better than domain walls at avoiding pinning while moved by electric current. Meanwhile, ferromagnetic skyrmions still have disadvantages such as the presence of stray fields and transverse dynamics, making them harder to employ for spintronic applications. In this work, we propose a novel topological object: the antiferromagnetic (AFM) skyrmion. This topological texture has no stray fields and we show that its dynamics are faster compared to its ferromagnetic analogue. We obtain the dependence of AFM skyrmion radius on the strength of Dzyaloshinskii-Moriya interaction coming from relativistic spin-orbit effects and temperature. We find that the thermal properties, e.g. such as the AFM skyrmion radius and diffusion constant, are rather different from those for ferromagnetic skyrmions. More importantly, we show that due to unusual topology the AFM skyrmions do not have a velocity component transverse to the current and thus may be perfect candidates for spintronic applications.

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement Renyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. In this talk I will show how topological phase transitions in 2d systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, I will present an efficient tensor network algorithm based on Projected Entangled Pair States (PEPS) to compute this quantity for a torus partitioned into cylinders, and then use this method to find sharp evidence of topological phase transitions in 2d systems with a string-tension perturbation. When compared to tensor network methods for Renyi entropies, this approach produces almost perfect accuracies close to criticality and, on top, is orders of magnitude faster. Moreover, I will show how the method also allows the identification of Minimally Entangled States (MES), thus providing a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states. If time allows I will also present briefly other ongoing projects at our group involving the use of tensor networks to study large-spin Kagome quantum antiferromagnets, 1d symmetry-protected topological order, continuous unitary transformations, and (1+1)d lattice gauge theories.

In this talk, I will give an introduction to the phenomenon of many body localization and its differences from single particle Anderson localization. Then, I discuss our recent exact diagonalization results of the many body localization (MBL) transition in the random field Heisenberg chain and present in particular the energy vs disorder strength phase diagram that was obtained from various estimators. The phase boundary is strongly energy dependent, thus providing evidence for an extensive mobility edge. At low disorder strength, eigentstates are ergodic and can be described by GOE statistics, while in the strong field phase, they are localized and show Poisson statistics. In the MBL phase, the eigenstate thermalization hypothesis is no longer fulfilled. If time permits, I will provide an outlook on our current work, where we look at the exact time evolution of initial product states. Reference: Luitz, D. J., Laflorencie, N. & Alet, F. Many-body localization edge in the random-field Heisenberg chain. Phys. Rev. B 91, 081103 (2015).

While the problem of calculating critical exponents was believed to be essentially solved by some experts already in the 1980s, this does not hold true for metallic systems at present. In a recent study of the spin-fermion model [1], Sur and Lee have found the first renormalization group fixed point for a quantum-critical metal using an epsilon-expansion around $d=3$. The critical theory was shown to have a quasi-local boson and one-dimensional electrons. However, the nature of potential fixed points in the physical dimensionality $d=2$ and the values of critical exponents are an important open problem. In this talk, I will therefore present first attempts to tackle this problem within a Wilsonian-type renormalization group framework, where modes with decreasing momenta are integrated out successively. [1] Sur and Lee, PRB 91, 125136 (2015)

Kitaev's honeycomb model [1] is a quantum spin liquid, celebrated for both the richness of its physical features, and the fact that it admits an exact solution. The latter can be cast in terms of Majorana fermions living in the background of a static Z_2 gauge field. The gapped phase of this model exhibits Z_2 topological order, equivalent to that of the toric code. Its ground state is a featureless spin liquid whose nontrivial properties can be revealed by introducing lattice defects. In the talk I will show that certain kinds of lattice dislocations and bond defects in this originally Abelian system carry unpaired Majorana fermions [2,3]. Each pair of such defects gives rise to a non-local physical fermion mode, i.e. a topologically-protected qubit, made out of two Majorana modes connected by a Z_2 gauge string. The qubit's composition reveals the crucial role of the emergent gauge field, neglected in most treatments of the Kitaev model, in the physics of Majorana modes. I will demonstrate how the non-local fermion can be created or annihilated by winding a magnetic vortex around a defect. [1] A. Kitaev, Ann. Phys. 321, 2 (2006). [2] O. Petrova, P. Mellado, O. Tchernyshyov, Phys. Rev. B 88, 140405 (2013). [3] O. Petrova, P. Mellado, O. Tchernyshyov, Phys. Rev. B 90, 134404 (2014).

Topological states of matter present a wide variety of striking new phenomena, most prominently is the fractionalization of electrons. Their detection, however, is fundamentally complicated by the lack of any local order. While there are now several instances of candidate topological spin liquids, their identification remains challenging. Here, we address one of the key questions: How can a quantum spin liquid phase be diagnosed in experiments? We find that the dynamical response can serve as a valuable tool for diagnosing quantum spin liquids. We provide a complete and rarely available exact theoretical study of the dynamical structure factor and the inelastic Raman scattering response of a two-dimensional quantum spin liquid in Abelian and non-Abelian phases. We show that there are salient signatures of the Majorana fermions and gauge fluxes emerging in Kitaev's honeycomb model. Our analysis identifies new varieties of the venerable X-ray edge problem and explores connections to the physics of quantum quenches. A number of proposals suggest that some materials with strong spin-orbit coupling, e.g. {Na/Li}2IrO3 or alpha-RuCl3 compounds, realize some of the physics of the Kitaev model. We discuss the current experimental situation, recent measurements and explore more generally the effect of breaking the integrability on response functions of Kitaev spin liquids.

I will talk about two recent surprises in the quantum Monte Carlo (QMC) simulation of quantum phase transitions. Surprise one is the solution of a thirty years old sign problem by Huffman and Chandrasekharan. It enables us to study the fermionic quantum critical point of spinless Dirac fermions using unbiased continuous-time QMC simulations. Compatible results are also obtained from infinite projected entangled-pair states calculations. I will compare the numerical results with predictions of the Gross-Neveu theory and discuss their physical implications. Surprise two is a generic, efficient and elegant approach to compute fidelity susceptibility of correlated fermions, bosons, and quantum spin systems in modern QMC methods. It can be used to detect quantum phase transitions without any prior knowledge of the local order parameter. Using it I will shed light on the hypothetical spin-liquid phase in the Hubbard model on honeycomb lattice.

The Anti-deSitter/Conformal Field Theory (AdS/CFT) correspondence is a duality relating strongly correlated quantum field theories to classical gravity in one higher dimension. Although discovered in the context of string theory, it has more recently been applied to condensed matter physics, where it offers insight into strongly correlated systems at a quantum critical point. In this talk, I will briefly introduce the AdS/CFT correspondence and indicate the connection to condensed matter physics. I turn to the electron star, a model of a perfect fluid of charged fermions backreating onto the geometry. I will discuss the numerical results obtained by solving the resulting equations of motion. Then, I turn to a description of fermions in curved spacetime, after which I will consider the fermion equations of motion in the electron star background. Finally, as an outlook, I will mention several extensions of this model.

In this talk, I will be presenting the consequence of the coupling between magnetic and vibrational degrees of freedom in Non-Kramer Quantum Spin Ice models focusing on experimentally relevant signatures for this specific class of quantum spin liquid. First, I will introduce Quantum Spin Ice physics borrowing insights from its well-studied classical counterparts. In particular, our work will build on the assumption that the monopole excitations present in classical Spin Ice remains well-defined quasi-particles. Quantum fluctuations of the spins provide a coherent mechanism for the transport of monopoles and lead to the emergence of a U(1) gauge field and an associated gapless photon. I will briefly explain how the pseudospin living on the vertex of the pyrochlore lattice emerges from the combination of single-ion physics and crystal field symmetries and insist on the importance of its non-Kramer nature to couple linearly phonons. The coupling between magnetic and vibrational degrees of freedom will be introduce on physical grounds and its form will be inferred from simple symmetry arguments. The last part of the talk will be focused on the consequences of this coupling on sound absorption measurements emphasizing the major role of the gapless photon.

After the experimental realization of graphene by Novoselov and Geim in 2004, for which they were awarded the Nobel Prize to in 2010, the scattering theory of two-dimensional massless Dirac fermions has become relevant because of its role in understanding graphene's transport properties. The latter motivated Jhih-Sheng Wu and Michael M. Fogler to study the problem of scattering on a circular step-like potential barrier, which is assumed to be a model for a circular cluster of charged impurities. The aim of the talk is to make an overview of some main aspects of their recent article Scattering of two-dimensional massless Dirac electrons by a circular potential barrier [1]. In this publication the scattering problem was treated with respect to the values of two parameters, X and rho, characterizing the size and the strength of the barrier, respectively. For each combination of X and rho a suitable tool was found for studying the scattering problem. One of the article's conclusions is the fact that formation of circular clusters increases the conductivity compared to the case of randomly distributed impurities. [1] Jhih-Sheng Wu and Michael M. Fogler, Scattering of two-dimensional massless Dirac electrons by a circular potential barrier, arXiv: 1410.0272v1 1 Oct 2014.

Using unbiased quantum Monte Carlo simulations we investigate the quantum phase transitions in SU(N) Hubbard models on square and honeycomb lattices. We construct and measure dimensionless fermionic correlation and order parameter ratios, which provide precise and independent estimates for the couplings at which a mass gap opens in the single particle spectrum and at which the order sets in. Furthermore these correlation ratios prove to be highly sensitive to weak order and render the need of pinning fields unnecessary. In particular, we study the nature and location of the phase transition between the semi-metal and Mott insulating antiferromagnetic state in the SU(2) Hubbard model on the honeycomb as well as the potentially deconfined Neel to valence bond solid phase transition in the SU(6) Hubbard model on the square lattice.

Light-matter interaction has played a central role in understanding as well as engineering new states of matter. Reversible coupling of excitons and photons enabled groundbreaking results in condensation and superfluidity of nonequilibrium quasiparticles with a photonic component. We investigated such cavity-polaritons in the presence of a high-mobility two-dimensional electron gas, exhibiting strongly correlated phases. When the cavity was on resonance with the Fermi level, we observed previously unknown many-body physics associated with a dynamical hole-scattering potential. In finite magnetic fields, polaritons show distinct signatures of integer and fractional quantum Hall ground states. Our results lay the groundwork for probing nonequilibrium dynamics of quantum Hall states and exploiting the electron density dependence of polariton splitting so as to obtain ultrastrong optical nonlinearities.

We apply the functional renormalization group (FRG) method to describe ground state properties of frustrated spin-1/2 systems on two-dimensional lattices. In order to be able to use this technique we rewrite the spin operators in terms of pseudo fermions. The resulting fermionic model is then treated via FRG, which manages to sum up diagrammatic contributions in different interaction channels in infinite order. Calculating the magnetic spin susceptibility we determine the ground state phase diagrams of various frustrated spin systems. Thereby, we discuss models such as the J1-J2 Heisenberg model on the square lattice and the Kagome Heisenberg model. A specific focus will be on the iridate compound Li_2IrO_3, where experiments suggest a magnetically ordered ground state of incommensurate spiral type. Applying our FRG technique to an extended Heisenberg-Kitaev model we are able to develop a microscopic scenario for the exchange interactions in this compound, explaining the experimental findings.

Loops arises as long length description for many quantum problems, in particular for SU(n) magnets. An interesting scenario in this kind of problems is the so-called deconfined criticality, a transition between Néel and valence bond solid phases in 2D quantum magnets, where numerical studies support a continuous phase transition but also display strong violations of finite size scaling that are not yet understood. This scenario is also believed to describe the phase transition for classical magnets where hedgehogs are suppressed. Three dimensional completely-packed loop models were shown to describe the same features as quantum magnets in 2D and the phase transition between a Néel state and a valence bond liquid. By modifying these loop models we can drive them to a phase transition with the same features: a magnetic ordered phase where there are long loops and a paramagnetic phase where a lattice symmetry is broken. In common with the direct studies of quantum Hamiltonians, we find strong violations of scaling for the SU(2) case. We describe accurately these violations and reach larger sizes than previous studies, making use of a wide range of observables. However, we do not find any conventional signs of a first order transition.

In studies of quantum phases of matter, the entanglement entropy has established itself as an important practical resource. For example it is universal at one-dimensional quantum critical points: the leading term can be used to extract the central charge c of the underlying conformal field theory, and thus identify the universality class. I will show how an analogous information theoretic quantity defined for classical systems, the Renyi Mutual Information (RMI), can be used to access universality classes in 2d. In particular for a rectangle cut into two rectangles, the shape dependence of the RMI can be computed exactly and is proportional to c. I will also discuss how this Mutual information is related to the entanglement entropy of certain Resonating valence bond states in 2d, as well as other basis-dependent entropies in 1d quantum systems. In all cases, the information theoretic approach provides an efficient way of identifying the various competing orders in a given classical or quantum system.

The realization of cold ensembles of polar molecules has opened a new pathway to explore the dynamics of quantum many body systems with strong, long-range and anisotropic dipolar interactions. While theoretical studies have so far focused on the equilibrium phases in the highly degenerate quantum regime , I will focus in my talk on non-equilibirum dynamics in the regime where quantum and thermal fluctuations are of the same order of magnitude. I will present two proposals: i.) a study on the glass transition in the presence of quantum fluctuations and ii.) a study on quantum fluctuations in the hexatic phase. i.) I will show, how the glass phase can be prepared in a bilayer system of ultracold dipolar molecules and present results on classical and quantum glassy behavior, characterized by long tails in the relaxation time and dynamical heterogeneity. I will also present experimental accessible order parameters based on marker molecules, distinguished by properly chosen internal levels, and find quantum features of dynamical heterogeneity. ii.) The hexatic phase is an intermediate phase in two dimensional systems when going from the crystal to the liquid phase. I will present results on the influence of quantum fluctuations on the nature of the hexatic phase and methods that allow one to measure these effects in a setup with polar molecules.

The question whether Anderson insulators can persist to finite-strength interactions - a scenario dubbed many-body localization - has received a great deal of interest. We formulate a precise sense in which a single energy eigenstate of a Hamiltonian can be adiabatically connected to a state of a non-interacting Anderson insulator, and define a many-body localized phase based on this. We explore the possible consequences of this; the most striking is an area law for the entanglement entropy of almost all excited states in a many-body localized phase. We present the results of numerical calculations for a one-dimensional system of spinless fermions. Furthermore, we study the implications that many-body localization may have for topological phases and identify scenarios in which many-body localization can help to stabilize topological order at non-zero energy density. We also explore the ways in which a relatively small quantum computer could be leveraged to study many-body localization. We show that, in addition to studying time-evolution, a quantum computer can, in polynomial time, obtain eigenstates at arbitrary energies to sufficient accuracy that localization can be observed.