Department of Physics • University of Cologne

For this opening colloquium of the CRC183 summer school on "Machine Learning in Condensed Matter Physics" Lei Wang is going to give an overview talk on the topic.

This is the contributed session of the CRC 183 Summer School "Machine Learning in Condensed Matter Physics" We will have the following short talks: Geometry of learning neural quantum states Chae-Yeun Park (University of Cologne) Unsupervised Learning Universal Critical Behavior via the Intrinsic Dimension Tiago Mendes Santos (MPI PKS) Convolutional restricted Boltzmann machine aided Monte Carlo: An application to Ising and Kitaev models Daniel Alcalde Puente (Forschungszentrum Jülich) AI-assisted quantum many-body computation beyond Markov-chain Monte Carlo Hongyu Lu (University of Hong Kong) Learning Many-body Hamiltonians from Dynamical Data Frederik Wilde (FU Berlin) From observations to complexity of quantum states: an unsupervised learning approach Zala Lenarčič (Jožef Stefan Institute)

I will describe different mechanisms by which gravity emerges from 2D conformal field theory. This includes holography and kinematic space, both examples of emergent gravity from entanglement, as well as a more recently discovered mechanism that involves an irrelevant deformation of the conformal field theory.

The classical Heisenberg model in two spatial dimensions constitutes one of the most paradigmatic spin models, taking an important role in statistical and condensed matter physics to understand magnetism. Still, despite its paradigmatic character and the widely accepted ban of a (continuous) spontaneous symmetry breaking, controversies remain whether the model exhibits a phase transition at finite temperature. Importantly, the model can be interpreted as a lattice discretization of the O(3) non-linear sigma model in (1+1) dimensions, one of the simplest quantum field theories encompassing crucial features of celebrated higher-dimensional ones (like quantum chromodynamics in (3+1) dimensions), namely the phenomenon of asymptotic freedom. This should also exclude finite-temperature transitions, but lattice effects might play a significant role in correcting the mainstream picture. In this work, we make use of state-of-the-art tensor network approaches, representing the classical partition function in the thermodynamic limit over a large range of temperatures, to comprehensively explore the correlation structure for Gibbs states. By implementing an SU(2)-symmetry in our two-dimensional tensor network contraction scheme, we are able to handle very large effective bond dimensions of the environment up to 1500, a feature that is crucial in detecting phase transitions. With decreasing temperatures, we find a rapidly diverging correlation length, whose behaviour is apparently compatible with the two main contradictory hypotheses known in the literature, namely a finite-T transition and asymptotic freedom.

The rich phenomenology of twisted bilayer graphene (TBG) near the magic angle is believed to arise from electron correlations in topological flat bands. An unbiased approach to this problem is highly desirable, but also particularly challenging, given the multiple electron flavors, the topological obstruction to defining tight binding models and the long-ranged Coulomb interactions. While numerical simulations of realistic models have thus far been confined to zero temperature, typically excluding some spin or valley species, analytic progress has relied on fixed point models away from the realistic limit. Here we present for the first time unbiased Monte Carlo simulations of realistic models of magic angle TBG at charge-neutrality. We establish the absence of a sign problem for this model in a momentum space approach, and describe a computationally tractable formulation that applies even on breaking chiral symmetry and including band dispersion. Our results include (i) the emergence of an insulating Kramers inter-valley coherent ground state in competition with a correlated semi-metal phase, (ii) detailed temperature evolution of order parameters and electronic spectral functions which reveal a `pseudogap' regime, in which gap features are established at a higher temperature than the onset of order and (iii) predictions for electronic tunneling spectra and their evolution with temperature. Our results pave the way towards uncovering the physics of magic angle graphene through exact simulations of over a hundred electrons across a wide temperature range. This work has been recently uploaded to ArXiv: 2105.12112

I will examine the role of topological ideas in understanding semimetals, gapless phases whose Fermi surfaces may be shrunk to isolated point nodes. First, I will review the theory of ‘Weyl semimetals’ that arise from accidental degeneracies in 3D crystals, and explore the consequences of the resulting band topology. I will show that the interplay of crystal symmetry and topology can aid in identifying “filling-enforced” semimetals, including in strongly correlated systems such as heavy fermion materials. I will also sketch how the topological underpinnings of these gapless phases may be probed experimentally via transport and spectroscopy, and through numerical simulations of their descendant gapped phases. References: Nat. Phys. 9, 299 (2013); PRX 4, 031035 (2014) ; PRX 5, 041046 (2015); PRB 94, 125122 (2016); arXiv:1508.01546, 1609.04023.

Weyl semimetals (WSMs) are a class of gapless topological materials which have gained a lot of interest in the last few years. In these states of matter, low-energy excitations behave as chiral massless particles, i.e. Weyl fermions. Besides exhibiting anomalous transport effects, the most prominent feature of these crystals are topologically protected surface states, the so-called Fermi arcs. Their emergence can be tied to an effective axial magnetic field arising at a surface due to lattice deformations and inducing a surface current by the chiral magnetic effect. Using a holographic model, I computed these currents in the strong coupling limit. The results show that the bulk-boundary correspondence in WSMs is in some sense independent of interactions demonstrating the universality of anomaly-related effects. In the end, I will discuss the limits of this universality. See also arXiv:1612.00836.