Condensed Matter

I will discuss our recent work on the use of autoregressive neural networks for many-body physics. In particular, I will discuss two approaches to represent quantum states using these models and their applications to the reconstruction of quantum states, the simulation of real-time dynamics of open quantum systems, and the approximation of ground states of many-body systems displaying long-range order, frustration, and topological order. Finally, I will discuss how annealing in these systems can be used for combinatorial optimization where we observe solutions to problems that are orders of magnitude more accurate than simulated and simulated quantum annealing.

"The relatively weak van der Waals bond in 2D materials has ushered in a rich new era of stacking engineering. We recently found in rhombohedrally stacked MoS2, a Berry phase contrast between layers can induce an asymmetric interlayer coupling and an out-of-plane spontaneous electrical polarization (1). The polarization direction can be switched via interlayer sliding, forming a new type of ferroelectricity. In addition, we demonstrated that such a polarization can lead to a spontaneous photovoltaic effect without any pn junctions (2). Compared to conventional PV effects, our device shows a similar quantum efficiency with an ultrafast speed and potentially a programmable polarity. The rhombohedrally stacked transition metal dichalcogenides therefore provide a new platform for studying spontaneous polarization at the atomic scale. (1) Jing Liang, et al, arXiv:2209.06966 (2022). (2) Dongyang Yang, et al, Nature Photonics, 16, 469–474 (2022)."

Structures composed of two monolayer-thin d-wave superconductors with a twist angle close to 45° are predicted to form a robust, fully gapped topological superconducting phase with spontaneously broken time-reversal symmetry and protected chiral edge modes. In this talk I will briefly review the theory behind the topological phase and discuss recent experimental efforts to fabricate and probe twisted flakes of high-Tc cuprate Bi2Sr2CaCu2O8+δ. Signatures of d-wave symmetry and of spontaneous T-breaking are indeed visible in the device Josephson current response, as detected through Fraunhofer pattern and Shapiro step analysis, and, very recently, a pronounced superconducting diode effect observed in samples near 45° twist but absent in untwisted samples.

In non-relativistic systems, the Lieb-Robinson Theorem imposes an emergent speed limit (independent of the relativistic limit set by c), establishing locality under unitary quantum dynamics and constraining the time needed to perform useful quantum tasks. We have extended the Lieb-Robinson Theorem to quantum dynamics with measurements. In contrast to the general expectation that measurements can arbitrarily violate spatial locality, we find at most an (M+1)-fold enhancement to the speed of quantum information, provided the outcomes of M local measurements are known; this holds even when classical communication is instantaneous. Our bound is asymptotically optimal, and saturated by existing measurement-based protocols (the "quantum repeater").  Our bound tightly constrain the resource requirements for quantum computation, error correction, teleportation, generating entangled resource states (Bell, GHZ, W, and spin-squeezed states), and preparing SPT states from short-range entangled states.

Zoom Link: https://pitp.zoom.us/j/95640053536?pwd=Z05oWlFRSEFTZWFRK2dwcHdsWlBBdz09

In this talk I will explore perspectives of quantum entanglement in (1+1)-d systems in presence of defects. The talk consists of two parts. In the first part, I will talk about the ground state entanglement entropy for 1d quantum spin chains with defects, using the transverse field Ising model and the three-state Potts model as examples. In the second part, I will describe the field theoretical replica trick approach to study entanglement entropy in such systems. This talk consists of some reviews about existing work, as well as work in progress with Linnea Grans-Samuelsson, Ananda Roy, Hubert Saleur, and Yifan Wang.

Zoom link: https://pitp.zoom.us/j/93049110080?pwd=QmpneGs2QlpZMlBROUlvU3VzaGtsZz09

 

The Entanglement Bootstrap is a program to derive the universal properties of a phase of matter from a single representative wavefunction on a topologically-trivial region.  Much (perhaps all) of the structure of topological quantum field theory can be extracted starting from a state satisfying two axioms that implement the area law for entanglement.  This talk will focus on recent progress (with Bowen Shi and Jin-Long Huang) using this approach to prove remote detectability of topological excitations in various dimensions.  This is an axiom of topological field theory.  Two key ideas are a quantum avatar of Kirby's torus trick to construct states on closed manifolds, and the new concept of pairing manifold, which is a closed manifold associated with a pair of conjugate excitation types that encodes their braiding matrix.  The pairing manifold also produces Verlinde formulae relating the S-matrix to the structure constants of a generalized symmetry algebra of flexible operators.  

Zoom link:  https://pitp.zoom.us/j/92633473610?pwd=eEhqR3BaQXljQm5ScHZvZm81N2FyZz09

The modular commutator is a recently discovered multipartite entanglement measure that quantifies the chirality of the underlying many-body quantum state. In this Letter, we derive a universal expression for the modular commutator in conformal field theories in 1+1 dimensions and discuss its salient features. We show that the modular commutator depends only on the chiral central charge and the conformal cross ratio. We test this formula for a gapped (2+1)-dimensional system with a chiral edge, i.e., the quantum Hall state, and observe excellent agreement with numerical simulations. Furthermore, we propose a geometric dual for the modular commutator in certain preferred states of the AdS/CFT correspondence. For these states, we argue that the modular commutator can be obtained from a set of crossing angles between intersecting Ryu-Takayanagi surfaces.

Zoom link:  https://pitp.zoom.us/j/94069836709?pwd=RlA2ZUsxdXlPTlh2TStObHFDNUY0Zz09

Google's TPUs were exclusively designed to accelerate and scale up machine learning workloads, amid the ongoing planet-wide race to build faster specialized hardware for artificial intelligence. But one must surely be able to use this hardware for other challenging computational tasks, right? We explored how to turn a TPU pod (2048 TPU v3 cores) into a dense linear algebra supercomputer to e.g. multiply two matrices of size 1,000,000 x 1,000,000 in just 2 minutes. We then used this power to perform a number of quantum physics and quantum chemistry computations at scale. For instance, we recently completed two largest-ever computations: a Density Functional Theory DFT computation of electronic structure (with N = 248,000 orbitals), and a Density Matrix Renormalization Group DMRG computation (with bond dimension D = 65,000). Cloud-based TPU pods and GPU pods are accessible to anyone and are poised to revolutionize the scientific supercomputing landscape.

Zoom link:  https://pitp.zoom.us/j/97006251134?pwd=WHhLa2pRUno0LzJjbzVnL2tsdGhOUT09

New quantum simulation platforms provide an unprecedented microscopic perspective on the structure of strongly correlated quantum matter. This allows to revisit decade-old problems from a fresh perspective, such as the two-dimensional Fermi-Hubbard model, believed to describe the physics underlying high-temperature superconductivity. In order to fully use the experimental as well as numerical capabilities available today, we need to go beyond conventional observables, such as one- and two-point correlation functions. In this talk, I will give an overview of recent results on the Hubbard model obtained through novel analysis tools: using machine learning techniques to analyze quantum gas microscopy data allows us to take into account all available information and compare different theories on a microscopic level. In particular, we consider Anderson's RVB paradigm to the geometric string theory, which takes the interplay of spin and charge degrees of freedom microscopically into account. The analysis of data from quantum simulation experiments of the doped Fermi-Hubbard model shows a qualitative change in behavior around 20% doping, up to where the geometric string theory captures the experimental data better. This microscopic understanding of the low doping limit has led us to the discovery of a binding mechanism in so-called mixed-dimensional systems, which has enabled the observation of pairing of charge carriers in cold atom experiments.
Intriguingly, mixed-dimensional systems exhibit similar features as the original two-dimensional model, e.g. a stripe phase at low temperatures. At intermediate to high temperatures, we use Hamiltonian reconstruction tools to quantify the frustration in the spin sector induced by the hole motion and find that the spin background is best described by a highly frustrated J1-J2 model.

Zoom link:  https://pitp.zoom.us/j/99449352935?pwd=cXdYYTJ2c1hVZ014SWRwZi9LRjQ3dz09

Superconductivity in electronic systems, where the non-interacting bandwidth for a set of isolated bands is small compared to the scale of the interactions, is a non-perturbative problem. Here we present a theoretical framework for computing the electromagnetic response in the limit of zero frequency and vanishing wavenumber  for the interacting problem, which controls the superconducting phase stiffness, without resorting to any mean-field approximation. Importantly, the contribution to the phase stiffness arises from (i) ``integrating-out" the remote bands that couple to the microscopic current operator, and (ii) the density-density interactions projected on to the isolated bands. We also obtain the electromagnetic response directly in the limit of an infinite gap to the remote bands, using the appropriate ``projected" gauge-transformations. These results can be used to obtain a conservative upper bound on the phase stiffness, and relatedly the superconducting transition temperature, with a few assumptions. In a companion article, we apply this formalism to a host of topologically (non-)trivial ``flat-band" systems, including twisted bilayer graphene. 

Zoom link:  https://pitp.zoom.us/j/99631762791?pwd=dU4yaU1wKzJNTisrazJjaUF2ODlXUT09

Topology has become a powerful tool to classify and understand materials. The standard paradigm divides the energy bands into two groups separated by a gap, or with at most some low-dimensional band crossings. Single-gap topological materials include topological insulators, Chern insulators, and topological semimetals. Recent work has extended these ideas to multi-gap systems, in which the energy bands are separated into three or more groups. The resulting phases can be characterized using the Euler class, and exhibit some interesting properties such as non-Abelian charges in the bulk.

In this talk, I will describe our work using first principles calculations to explore topological phases in materials, including both electronic and phononic spectra. In the context of single-gap topology, I will describe the interplay between temperature and topology in electronic systems; while in the context of multi-gap topology, I will present the manipulation of non-Abelian band nodes in phononic systems.

Zoom Link: https://pitp.zoom.us/j/93085720537?pwd=RlhrVFJZU1RmY284Nm5xUXRJakdMZz09

I discuss how exact, non-perturbative results can be obtained for both optical transport and static susceptibilities in “Hertz-Millis” theories of Fermi surfaces coupled to critical bosons. Such models possess a large emergent symmetry and anomaly structure, which we leverage to fix these quantities. In particular, I will show that in the infrared limit, the boson self energy at zero wave vector is a constant independent of frequency, and the real part of the optical conductivity is purely a delta function Drude peak with no other corrections. I will also obtain exact relations between Fermi liquid parameters as the critical point is approached from the disordered phase. 

Zoom Link:  https://pitp.zoom.us/j/93340611986?pwd=cisrZmFxcEVWZVdrT2tMRVZiVTdRQT09