Quantum Matter

High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat  the electron interactions.  Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity.  In 1992 Hatsugai and Khomoto wrote down a momentum-space model for a Mott insulator which is safe to say was largely overlooked, their paper garnering just 21 citations (6 due to our group).  I will show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper's instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity.  The properties of the superconducting state differ drastically from that of the standard BCS theory.  The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state.

Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.

[1] https://www.nature.com/articles/s41567-020-0988-4.

Twisted bilayer graphene (tBLG) is a host to a variety of electronic phases, most notably superconductivity when doped away from putative correlated insulator phases. In order to understand the nature of those phases, numerical simulations such as Hartree-Fock calculation and density matrix renormalization group (DMRG) techniques are essential.

Due to the long-range Coulomb interaction and its fragile topology, however, tBLG is difficult to study with standard DMRG techniques.

In this work, we present how a recently developed MPO compression algorithm can be used to make the problem tractable, and how 1D Wannier localization can be used to circumvent the fragile topology.

As a test case, we apply this technique to the toy model of spinless/single-valley model of tBLG. We find that the ground state is essentially a k-space Slater determinant, confirming the validity of previous Hartree-Fock calculations. If time permits, I will also present our ongoing effort to apply this technique to spinful/valleyful model for tBLG.

The quest for non-Abelian quasiparticles has inspired decades of experimental and theoretical efforts. Among their clearest signatures is a thermal Hall conductance with quantized half-integer value. Such a value was indeed recently observed in a quantum-Hall system at ν=5/2 and in the magnetic insulator α-RuCl3. I will explain that a non-topological "thermal metal" phase that forms due to quenched disorder may disguise as a non-Abelian phase by well approximating the trademark quantized thermal Hall response. Remarkably, the quantization here improves with temperature, in contrast to fully gapped systems. In my talk, I will provide analytical and numerical evidence for this effect and discuss its possible implications for the aforementioned experiments.

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.

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.

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.

I’ll talk about two independent works on classical and quantum neural networks connected by information theory. In the first part of the talk, I’ll treat sequence models as one-dimensional classical statistical mechanical systems and analyze the scaling behavior of mutual information. I'll provide a new perspective on why recurrent neural networks are not good at natural language processing. In the second part of the talk, I’ll study information scrambling dynamics when quantum neural networks are trained by classical gradient descent algorithm. For many problems, this hybrid quantum-classical training process consists of two stages where information scrambles very differently in the network. 

I propose [1] to use the residual anyons of overscreened Kondo physics for quantum computation. A superconducting proximity gap of Δ<TK can be utilized to isolate the anyon from the continuum of excitations and stabilize the non-trivial fixed point. We use the dynamical large-N technique [2] and bosonization to show that the residual entropy survives in a superconductor and suggest a charge Kondo setup for isolating and detecting the Majorana fermion in the two-channel Kondo impurity.
I will then conjecture that topological defects in a multichannel Kondo lattice carry anyons. Motivated by this, we look at a two-channel SU(N) Kondo lattice in the large-N limit [3].  In this model, the continuous channel-symmetry is spontaneously broken, forming a “channel ferromagnet” and realizing the so-called fractionalized order parameter [4]. By integrating out the fermions we derive an effective action that describes the symmetry breaking and its emergent collective modes. Remarkably, topological defects in the order parameter carry a U(1) flux, manifested in the Aharonov-Bohm phase picked by electrons that orbit the defect. We argue that the phase diagram contains a non-magnetic transition between a large and a small Fermi surface.
I will also briefly highlight our recent results [5] on a magnetically frustrated Kondo-screened triangle which contains two symmetry-preserving phases, transcending the Landau-Ginzburg paradigm. The quantum phase transition is driven by the proliferation of instantons of the emergent gauge theory and can be regarded as a toy model for the deconfined criticality.