Condensed Matter

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.

Meta-learning involves learning mathematical devices using problem instances as training data. In this talk, we first describe recent meta-learning approaches involving the learning of objects such as: initial weights, parameterized losses, hyper-parameter search strategies, and samplers. We then discuss learned optimizers in further detail and their applications towards optimizing variational circuits. This talk also covers some lessons learned starting a spin-off from academia.

In this talk I will discuss effective field theories for two classes of non-equilibrium systems, one far and one near equilibrium. The backbone of the approach is the Schwinger-Keldysh formalism, which is the natural starting point for doing field theory in non-equilibrium situations. In the first part of the talk I will present an effective response for topological driven (Floquet) systems, which are inherently far from equilibrium. As an example, I will discuss a chiral Floquet drive coupled to a background $U(1)$ field, which gives rise to a theta term in the response action, and show that this is independent of smooth deformations of the underlying system. In the second part, I will discuss an ongoing project using effective field theories for hydrodynamics. I will show that chiral diffusion for interacting systems in 1+1 dimensions, which may be relevant to edge transport in quantum Hall systems, has an infrared instability. I will then discuss the fate of this instability.

The first part of this talk will introduce generalized Jordan–Wigner
transformation on arbitrary triangulation of any simply connected
manifold in 2d, 3d and general dimensions. This gives a duality
between all fermionic systems and a new class of Z2 lattice gauge
theories. This map preserves the locality and has an explicit
dependence on the second Stiefel–Whitney class and a choice of spin
structure on the manifold. In the Euclidean picture, this mapping is
exactly equivalent to introducing topological terms (Chern-Simon term
in 2d or the Steenrod square term in general) to the Euclidean action.
We can increase the code distance of this mapping, such that this
mapping can correct all 1-qubit and 2-qubits errors and is useful for
the simulation of fermions on the quantum computer. The second part of
my talk is about SPT phases. By the boson-fermion duality, we are able
to show the equivalent between any supercohomology fermionic SPT and
some higher-group bosonic SPT phases. Particularly in (3+1)D, we have
constructed a unitary quantum circuit for any supercohomology
fermionic SPT state with gapped boundary construction. This fermionic
SPT state is derived by gauging higher-form Z2 symmetry in the
higher-group bosonic SPT and apply the boson-fermion duality.

I will briefly review the pseudogap phenomenology in high Tc cuprate superconductor, especially the recent experiments, and propose a unified picture of the phenomenology under only one assumption: the fluctuating pair density wave. By quantum disordering a pair density wave, we found a state composed of insulating antinodal pairs and nodal electron pocket. We compare the theoretical predictions with ARPES results, optical conductivity, quantum oscillation and other experiments.

We derive general results relating revivals in the dynamics of quantum
many-body systems to the entanglement properties of energy eigenstates.
For a D-dimensional lattice system of N sites initialized in a
low-entangled and short-range correlated state, our results show that a
perfect revival of the state after a time at most poly(N) implies the
existence of "quantum many-body scars", whose number grows at least as
the square root of N up to poly-logarithmic factors. These are energy
eigenstates with energies placed in an equally-spaced ladder and with
Rényi entanglement entropy scaling as log(N) plus an area law term for
any region of the lattice. This shows that quantum many-body scars are a
necessary condition for revivals, independent of particularities of the
Hamiltonian leading to them. We also present results for approximate
revivals, for revivals of expectation values of observables and prove
that the duration of revivals of states has to become vanishingly short
with increasing system size.

Work in collaboration with Henrik Wilming (ETH)