Condensed Matter

The sign problem is a widespread numerical hurdle preventing us from simulating the equilibrium behaviour of many interesting models, most notably the Hubbard model. Research aimed at solving the sign problem, via various clever manipulations, has been thriving for a long time with various recent exciting results. The complementary question, of whether some phases of matter forbid the existence of any sign-free microscopic model, has received attention only recently. In this talk, I’ll review recent progress and discuss a novel and quite general criteria we obtained for when a topological quantum field theory has no sign-free microscopic model. I’ll also point out relations to sign problems in frustrated magnets and to the notion of quantum supremacy.

Condensed matter physics is the study of the complex behaviour of a large number of interacting particles such that their collective behaviour gives rise to emergent properties. We will discuss some interesting quantum condensed matter systems where their intriguing emergent phenomena arise due to strong coupling. We will revisit the Landau paradigm of Fermi liquid theory and hence understand the properties of the non-Fermi liquid systems which cannot be described within the Landau framework, due to the destruction of the Landau quasiparticles. In particular, we will focus on critical Fermi surface states, where there is a well-defined Fermi surface, but no quasiparticles, as a result of the strong interactions between the Fermi surface and some massless boson(s). We will outline a framework to extract the low-energy physics of such systems in a controlled approximation, using the tool of dimensional regularization.

In this talk, I will discuss emergent criticality in non-unitary random quantum dynamics. More specifically, I will focus on a class of free fermion random circuit models in one spatial dimension. I will show that after sufficient time evolution, the steady states have logarithmic violations of the entanglement area law and power law

correlation functions. Moreover, starting with a short-range entangled many-body state, the dynamical evolution of entanglement and correlations quantitatively agrees with the predictions of two-dimensional conformal field theory with a space-like time direction. I will argue that this behavior is generic in non-unitary free quantum dynamics with time-dependent randomness, and show that the emergent conformal dynamics of two-point functions arises out of a simple" nonlinear master equation".

Recently, a lot of attention has been dedicated to a novel class of topological systems, called higher-order topological insulators (TIs). The reason is that, while a conventional d-dimensional TI exhibits (d-1)-dimensional gapless boundary modes, a d-dimensional nth-order TI hosts gapless modes at its (d-n)-dimensional boundaries only, generalizing in this way the notion of bulk-boundary correspondence. In this talk I will show the results of our recent study of such systems in two and three dimensions. I will briefly describe a few specific proposals to engineer such systems in practice. I will also present a simple method which can be used to read out the resulting topological phase diagrams experimentally. I will conclude by saying why the higher-order TIs are promising to study the interplay of topology and interactions and how Machine learning can help us to better understand these novel topological states.

We propose a reinforcement learning (RL) scheme for feedback quantum control within the quantum approximate optimization algorithm (QAOA). QAOA requires a variational minimization for states constructed by applying a sequence of unitary operators, depending on parameters living in a highly dimensional space. We reformulate such a minimum search as a learning task, where a RL agent chooses the control parameters for the unitaries, given partial information on the system. We show that our RL scheme learns a policy converging to the optimal adiabatic solution for QAOA found by Mbeng et al. arXiv:1906.08948 for the translationally invariant quantum Ising chain. In presence of disorder, we show that our RL scheme allows the training part to be performed on small samples, and transferred successfully on larger systems. Finally, we discuss QAOA on the p-spsin model and how its robustness is enhanced by reinforce learning. Despite the possibility of finding the ground state with polynomial resources even in the presence of a first order phase transition, local optimizations in the p-spsin model suffer from the presence of many minima in the energy landscape. RL helps to find regular solutions that can be generalized to larger systems and make the optimization less sensitive to noise.

References

https://arxiv.org/abs/2003.07419

https://arxiv.org/abs/2004.12323

Stacking two graphene layers twisted by the ‘magic angle’ 1.1º generates flat energy bands, which in turn catalyzes various strongly correlated phenomena depending on filling and sample details. While this system is most famous for the superconducting and insulating states observed at fractional fillings, I argue that charge neutrality presents an interesting interplay of disorder and interactions.

In scanning tunnelling microscopy (STM), the most striking signature of interactions occurs close to charge neutrality, where the splitting between the flat bands increases dramatically. In analogy with quantum Hall ferromagnetism, I show that this effect may be qualitatively understood as the result of an exchange energy gain. A low-energy manifold of gapped, symmetry-breaking states is identified, one of which possesses quantum valley Hall order. Transport measurements yield ostensibly conflicting information at charge neutrality: while some samples reveal semimetallicity (as expected when correlations are weak), yet others exhibit robust insulation. I reconcile these observations and those of STM by arguing that strong interactions supplemented by weak, smooth disorder stabilize a network of locally gapped quantum valley Hall domains with spatially varying Chern numbers determined by the disorder landscape—--even when an entirely different order is favored in the clean limit. I conclude with a discussion of experimental tests of this proposal via local probes and transport.

The average entanglement entropy of subsystems of random pure states is (nearly) maximal. In this talk, we discuss the average entanglement entropy of subsystems of highly excited eigenstates of integrable and nonintegrable many-body lattice Hamiltonians. For translationally invariant quadratic models (or spin models mappable to them) we prove that, when the subsystem size is not a vanishing fraction of the entire system, the average eigenstate entanglement entropy exhibits a leading volume-law term that is different from that of random pure states. We argue that such a leading term is likely universal for translationally invariant (noninteracting and interacting) integrable models. For random pure states with a fixed particle number (random canonical states) away from half filling and normally distributed real coefficients, we prove that the deviation from the maximal value grows with the square root of the system's volume when the size of the subsystem is one half of that of the system. We then show that the average entanglement entropy of highly excited eigenstates of a particle number conserving quantum chaotic model is the same as that of random canonical states.

A scientific understanding of modern deep learning is still in its early stages. As a first step towards understanding the learning dynamics of neural networks, one can simplify the problem by studying limits that might have theoretical tractability and practical relevance. I’ll begin with a brief survey of our earlier body of work that has investigated the infinite width limit of deep networks, a topic of active study recently. With these results in hand, it nonetheless appears there is still a gap towards theoretically describing neural networks at finite width. I’ll argue that the choice of learning rate is one crucial factor in dynamics away from the infinite width limit and naturally classifies deep networks into two classes separated by a sharp transition. This is elucidated in a class of solvable simple models we present, which give quantitative predictions for the two classes. Quite remarkably, we test these predictions empirically in practical settings and find excellent agreement. 

Yasaman Bahri is a research scientist on the Google Brain team. Her current research program is to build a scientific understanding of deep learning using a combination of theoretical analysis and empirical investigation. Prior to Google, she was at the University of California, Berkeley, where she received her Ph.D. in physics in 2017, specializing in theoretical quantum condensed matter.

While the concept of topology is often introduced by contrasting oranges with bagels, the idea of topologically distinct quantum phases of matter is far more abstract. In this talk, we will focus on a more tangible form of topology that also arises in quantum condensed matter system: when the sites in a lattice are dragged around in a symmetric manner, what attributes of the lattice would remain unchanged? Such deformation can be viewed as the lattice analog of the familiar (mental) exercise of transforming a bagel into a coffee mug. We will first introduce the mathematical framework for identifying the topological classes of lattices, and then discuss how these invariants can constrain and inform the more abstract notion of topological phases of matter that emerge.

We discuss a new class of quantum phase transitions --- Deconfined Mott Transition (DMT) --- that describe a continuous transition between a Fermi liquid metal with a generic electronic Fermi surface and an insulator without emergent neutral Fermi surface. We construct a unified U(2) gauge theory to describe a variety of metallic and insulating phases, which include Fermi liquids, fractionalized Fermi liquids (FL*), conventional insulators and quantum spin liquids, as well as the quantum phase transitions between them. Using the DMT as a basic building block, we propose a distinct quantum phase transition --- Deconfined Metal-Metal Transition (DM2T) --- that describes a continuous transition between two metallic phases, accompanied by a jump in the size of their Fermi surfaces (also dubbed a 'Fermi transition'). We study these new classes of deconfined metallic quantum critical points using a renormalization group framework at the leading nontrivial order in a controlled double-expansion and comment on the various interesting scenarios that can emerge going beyond this leading order calculation.