Department of Physics • University of Cologne

Quantum anomalies of symmetries are a kind of old questions in quantum field theory, which have some new advancements over the past decades due to the development of topological phases of matter. In this talk, we will try to discuss some aspects of them in view of the topological phases of matter, including how to identify the anomaly of symmetry of a theory (in particular, 2+1D topological order) via so-called anomaly indicators, and some applications of the quantum anomaly—enforced symmetry breaking and construction of 1D lattice model with anomalous symmetry.

I am just testing the email and slack scripts

Reaction-diffusion models, where particles are allowed to react when they meet, display genuine non-equilibrium behaviour. In classical settings, it has been shown that universal properties arise, and that non-equilibrium steady-state phase transitions between fluctuating and absorbing phases can appear. Recent studies have shown that quantum dynamics can modify the properties of critical non-equilibrium systems, and that even the reaction-limited asymptotics cannot be properly described by a mean-field approximation. Starting from the quantum Master equation, we propose a field-theoretical approach to the study of quantum reaction-diffusion systems, building on the Keldysh formalism. We tackle the problem starting from the two-particle loss process A + A -> O. By means of a perturbative expansion, we exploit the Dyson equation in order to derive Boltzmann-like equations for the bosonic and fermionic particle densities. These are compared to the classical and quantum reaction-limited rate equations, and are solved both in the homogeneous and non-homogeneous case. We study the dynamics of a quench from a double- to a single-well confining potential, where a novel decay regime is reached.

In the field of monitored quantum circuits, it has remained an open question whether finite-time protocols for preparing long-range entangled (LRE) states lead to phases of matter which are stable to gate imperfections. Here we show that such gate imperfections effectively convert projective into weak measurements and that, in certain cases, long-range entanglement persists, even in the presence of weak measurements and gives rise to novel forms of quantum criticality. We demonstrate this explicitly for preparing the two-dimensional (2D) GHZ cat state and the three-dimensional (3D) toric code as minimal instances. In contrast to previous studies on measurement-induced phases and transitions, our circuit of gates and measurements is deterministic; the only randomness is in the measurement outcomes. We show how the randomness in these weak measurements allows us to track the solvable Nishimori line of the random-bond Ising model, rigorously establishing the stability of the glassy LRE states in two and three spatial dimensions. Away from this exactly solvable construction, we use hybrid tensor network and Monte Carlo simulations to obtain a non-zero Edwards-Anderson order parameter as an indicator of long-range entanglement in the 2D scenario. We argue that our protocol admits a natural implementation in existing quantum computing architectures, requiring only a depth-3 circuit on IBM's heavy-hexagon transmon chips.

Abstract: Hybrid light-matter excitations, so-called polaritons, combine the advantages of photons in detection and transmission with the interactions of their matter component. They are therefore not only of great technological interest but also promising tools to probe new states of matter. However, their driven and dissipative nature also poses a challenge for any theoretical description. In this talk I will explain how this challenge can be addressed with non-equilibrium field-theory. Using two examples from my recent research I will provide a small glimpse into the rich many-body physics of polaritons. I will begin by introducing a systematic expansion in the interaction range and leverage it to provide a quantitative description of non-equilibrium phase transitions in photonic waveguides. Subsequently I will address the time-evolution of polaron-polaritons in a two-dimensional semiconductor irradiated by an intense light pulse, highlighting our recent advances towards the quantitative description of the dynamics of highly excited many-body systems.

(Bachelor Colloquium)

We introduce a new version for the quantum version of the standard reinforcement learning benchmarking problem: the cartpole. The goal is to keep a wavefunction stable on top of an inverted potential, by applying weak measurements and feeding the results to a controller. Our approach shows, that even with minimal measurement information, it is possible to extend the lifetime of the wavefunction, by a significant margin. Our approach works for arbitrary potentials and due to weak measurements makes it feasible for experimental implementation.

Zoom-Link: https://uni-koeln.zoom.us/j/94816401656?pwd=ZXFNRVBKdFlyeW9pVWdQaHdUSFB3Zz09

In this talk I’ll talk about our ongoing research effort in understanding some type I fracton topological phases and phase transitions, by means of constructing exact tensor network ground state wave-functions and through the lens of duality. In recent years the 3D gapped fracton topological phases have attracted much attention motivated from various directions: the search for more robust topological quantum memory; generalization of gauge theory; and constrained dynamics. In this talk I’ll try to introduce some of the basic concepts in a pedagogical way and tell you the physical problems I’ve been considering: 1. phase transitions of fracton topological phases (beyond Landau paradigm); 2. possible fractonic extension of the Kitaev gapless spin liquid? I will share with you my evolving understanding for these questions from the perspective of exact tensor-network states, via quantum classical mapping and duality.

For a particle in a one-dimensional random potential all eigenstates are localized (Anderson localization). Interplay between interactions and disorder can lead to a localization-delocalization transition: in disordered bosonic fluids, the ground state is either a superfluid or in a localized phase called Bose glass. The associated phase diagram is well understood, but there is little study of the precise properties of the Bose-glass phase. Using a functional implementation of the Renormalization Group, I will describe the Bose-glass phase and some of its glassy properties linked to the existence of metastable states. I will then discuss the chaotic behavior of the Bose glass, i.e. its extreme sensitivity to external parameters. Finally, I will consider the effect of long-range interactions, which can induce a new disordered phase called Mott glass.

The speaker is online from home, but we could have an in-presence audience in the usual seminar room 0.03. See you tomorrow!

Bachelor colloquium

The outlook of protected quantum computing spurred enormous progress in the search for topological materials, sustaining a continued race to find the most experimentally feasible platform. Here, we show that one of the simplest quantum circuits, the Cooper-pair transistor, exhibits a nontrivial Chern number which has not yet been discussed, in spite of the exhaustive existing literature. Surprisingly, the resulting quantized current response is robust with respect to a large number of external perturbations, most notably low-frequency charge noise and quasiparticle poisoning. Moreover, the fact that the higher bands experience crossings with higher topological charge leads to all the bands having the same Chern number, such that there is no restriction to stay close to the ground state. Remaining small perturbations are investigated based on a generic Master equation approach. Finally, we discuss feasible protocols to measure the quantized current.

The title above constitutes the greatest common divisor of two topics that I plan to cover in this seminar: variational time evolution of neural quantum states to simulate open system dynamics [1] and a machine learning approach to study the complexity of quantum states [2]. [1] https://arxiv.org/abs/2104.00013 [2] https://arxiv.org/abs/2102.11328

A wave function exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement induced state updates, defining a quantum trajectory. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. However, due to the stochastic nature of the wave function this type of phase transition does not manifest itself in common observable averages, obtained from the statistically averaged density matrix, and have instead mainly been observed in the dynamics entanglement. Hence, they are often termed entanglement transitions. Here we establish a novel type of entanglement transition between a regime of logarithmic entanglement growth, and a quantum Zeno regime obeying an area law, in continuously monitored fermion dynamics. We analyze the phase transition from to different perspectives: (i) numerical simulations of monitored lattice fermions and (ii) an analytical field theory for monitored Dirac fermions, interpolating between the microscopic measurement dynamics and the macroscopic observables. We identify the relevant degrees of freedom for describing the phase transition and show that their dynamics is governed by a non-Hermitian quantum Sine-Gordon model. This yields a physical picture for the phase transition in terms of a depinning from the measurement operator eigenstates induced by unitary dynamics, and places it into the BKT universality class.

We discuss how the Tensor Network representation of classical statistical lattice models, with particular regards to the evaluation of the free energy, the entropy per site, and diverse correlation functions. We explain how the Corner Transfer Matrix (CTM) algorithm can be used for these sakes, and compare its results with those obtained via the Variational Uniform Matrix Product State (VUMPS) algorithm and the Tensor Renormalization Group (TRG) algorithm. In particular, we investigate whether tensor network methods are suitable to study frustrated systems, focussing here on the geometrically frustrated Ising antiferromagnetic model on the triangular lattice. We show that an accurate estimate of the non-trivial zero-point entropy can be obtained, and verify that the peculiar algebraic decay of the spin-spin correlation function with increasing distance can be faithfully reproduced. This gives us confidence to employ Tensor Networks to study classical spin liquids in the rest of this Master thesis.

Zoom Meeting: https://us04web.zoom.us/j/990289238?pwd=WEdGR2IvdTk4dlVYdW9lQTRXZUdRQT09 Meeting ID: 990 289 238 Password: 045204

I will talk about whether there is criticality in periodically driven systems. The motivation is based on the work done in [Phys. Rev. Lett. 122, 110602 (2019)]. This paper uses an RG approach and finds that criticality is absent in periodically driven open systems. This is interpreted as a second order phase transition becoming first order because of the drive. I will talk about dynamical classical system described by the φ4 theory with O(N) symmetry. I have included fluctuations in the presence of the periodic drive and calculated the corrections to the mass up to an infinite loop order within the Hartree approach. In the presence of a sufficiently strong periodic drive, I obtain multiple solutions for the correlation length [(mass)^(−1/2)]. One of them diverges at the transition but the other remains finite and hence, we conclude that the drive can indeed suppress criticality in these systems. In order to make further progress, I apply Hartree approximation to the φ6 theory, which is known to exhibits a first order phase transition. Multiple solutions for the correlation length emerge in a way that is very similar to the periodically driven system. This indicates that the transition can be changed from second to first order by the periodic drive.

The functional renormalization group (fRG) is a versatile, quantum-field-theoretical formulation of the powerful RG idea and has seen a large number of successful applications. The main limitation of this framework is the truncation of the hierarchy of flow equations, where typically effective three-particle interactions are neglected altogether. Here, we first present multiloop fRG flow equations [1] as a way of simulating all contributions of the six-point vertex that can be kept efficiently. The resulting flow consists of successive one-loop calculations and sums up a complete class of diagrams. This restores the independence of the results from the choice of regulator and enables improvement of many fRG computations. Second, we show how to derive the multiloop flow equations from the self-consistent parquet relations on an algebraic basis [2]. Using the X-ray-edge singularity as an example, we introduce the formalism and illustrate our findings with numerical results [3]. [1] F. B. Kugler and J. von Delft, PRB 97, 035162 (2018) [2] F. B. Kugler and J. von Delft, New J. Phys. 20, 123029 (2018) [3] F. B. Kugler and J. von Delft, PRL 120, 057403 (2018)

We investigate phase transitions in rapidly periodically driven, open quantum systems within a complex bosonic order parameter model with phase rotation symmetric drive. The infinitely rapidly driven limit is effectively stationary and exhibits a second order phase transition. Based on a Floquet renormalization group analysis, we reveal a universal mechanism showing that fluctuations associated to the first rotating wave correction mask the critical physics associated with the equilibrium fixed point. The critical exponents of the infinitely rapidly driven fixed point can be probed upon smoothly approaching it, in some analogy to the opposite limit of slowly driven systems within the Kibble-Zurek mechanism.

Master Colloquium

In one-dimensional Luttinger liquids the interaction strength is determined by the Luttinger Parameter K. It proves proves difficult to be measured, as it is usually hidden in power-law dependencies on temperature or bias. In this talk I will propose a setup, which allows a dynamical measurement of this parameter. In this talk we will, based on an equation of motion description of Luttinger Liquids, discuss a setup with a capacitive gate, which allows to probe the interactions directly. In this setup, an expression for the frequency dependence of the conductivity can be obtained, from which we can extract K directly and from a low frequency expansion. Furthermore the influence of the precise form of the change in interactions at the contacts is examined using the formalism. As a perfectly suited system to test the predictions, we will shortly discuss helical edge states of topological insulators.

The Kitaev model is an exactly-soluble quantum spin model with frustration. Although the original model was defined on a honeycomb lattice, the model has been extended to various tricoordinate lattices without losing the exact solubility. We analyze two different anisotropic limits of the Kitaev model on a three-dimensional lattice comprising nine-site elementary loops, which we call the hypernonagon lattice. In both cases, the effective Ising-type models retain the time-reversal symmetry, suggesting that the ground states are chiral spin liquids. Using Monte Carlo simulations that respect the local and global constraints on the Ising variables representing Z2 fluxes, we show that there is a first-order phase transition at a finite temperature in each case, but in a different manner.

Modern data analysis requires computations on massive data. For example, consider the problem of automatically classifying articles in a huge digital archive containing millions of entries, or recommending items to millions of users based on their purchase history. Bayesian probabilistic modeling allows us to make assumptions about hidden structure in the data that is not directly observable. In Bayesian inference, we fit a probability distribution that reveals this structure. Bayesian inference has been inspired by theoretical physics over many years, a prominent example being Markov Chain Monte Carlo algorithms. In a more recent approach called variational inference, Bayesian inference is mapped to an optimization problem. Here, we fit a parametrized 'mean field' distribution by optimizing over variational parameters in a way to maximize the statistical evidence of the data. This method scales up to massive data sets when using stochastic optimization, termed stochastic variational inference (SVI). SVI uses easy-to-compute noisy gradients by subsampling from the large underlying data set. It suffers from two major problems: noisy gradients and non-convexity. We introduce a scheme that reduces the noise by averaging over parts of the past gradients. This introduces a bias, and we discuss the tradeoff between variance and bias. To enable convergence to better local optima, we introduce deterministic annealing for SVI. We introduce a temperature parameter that deterministically deforms the objective, and then reduce this parameter over the course of the optimization. We test both methods on Latent Dirichlet Allocation, a topic model, applied to three large text corpora.

Functional renormalization group (fRG) methods relate theories at different energy scales via an exact flow equation for a functional of the fields. In this talk, I will focus on a one-particle irreducible, purely fermionic formulation and, in particular, on its application to phases of broken symmetries and multiband Hubbard models. First, I will report on a recent fRG study on antiferromagnetic ordering in a simple two-pocket model, including a possible extension to coexistence phases of antiferromagnetism and superconductivity. The second part will be devoted to multiband systems. Particularities of the point-group behavior of multiband Hubbard models are discussed and fRG results are presented for a generic three-band model for the cuprate superconductors. Finally, an outlook on a potentially highly parallelizable fRG algorithm is given, which should be suitable for calculations with a larger number of bands.