This series consists of talks in the area of Condensed Matter.
Quantum Monte Carlo methods, when applicable, offer reliable ways to extract the nonperturbative physics of strongly-correlated many-body systems. However, there are some bottlenecks to the applicability of these methods including the sign problem and algorithmic update inefficiencies. Using the t-V model Hamiltonian as the example, I demonstrate how the Fermion Bag Approach--originally developed in the context of lattice field theories--has aided in solving the sign problem for this model as well as aided in developing a more efficient algorithm to study the model.
Periodically driven (Floquet) systems can display entirely new many-body phases of matter that have no analog in stationary systems. One such phase is the Floquet time crystal, which spontaneously breaks a discrete time-translation symmetry. In this talk, I will survey the physics of these new phases of matter. I explain how they can be stabilized either through strong quenched disorder (many-body localization), or alternatively in clean systems in a "prethermal" regime which persists until a time that is exponentially long in a small parameter.
"Recently, exactly solvable 3D lattice models have been discovered for a new kind of phase, dubbed fracton topological order, in which the topological excitations are immobile or are bound to lines or surfaces. Unlike liquid topologically ordered phases (e.g. Z_2 gauge theory), which are only sensitive to topology (e.g. the ground state degeneracy only depends on the topology of spatial manifold), fracton orders are also sensitive to the geometry of the lattice. This geometry dependence allows for remarkably new physics which was forbidden in topologically invariant phases of matter.
I will describe the recently developed bimetric theory of fractional quantum Hall states. It is an effective theory that includes the Chern-Simons term that describes the topological properties of the fractional quantum Hall state, and a non-linear, a la bimetric massive gravity action that describes gapped Girvin-MacDonald-Platzman mode at long wavelengths.
Quantum critical points (QCP) beyond the Landau-Ginzburg paradigm are often called unconventional QCPs. There are in general two types of unconventional QCP: type I are QCPs between ordered phases that spontaneously break very different symmetries, and type II involve topological (or quasi-topological) phases on at least one side of the QCP. Recently significant progress has been made in understanding (2+1)-dimensional unconventional QCPs, using the recently developed (2+1)d dualities, i.e., seemingly different theories may actually be identical in the infrared limit.
Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state.
Two seemingly different quantum field theories may secretly describe the same underlying physics — a phenomenon known as “duality". I will review some recent developments in field theory dualities in (2+1) dimensions and some of their applications in condensed matter physics, in particular in quantum Hall effect and quantum phase transitions.
Clean and interacting periodically driven quantum systems are believed to exhibit a single, trivial “infinite-temperature” Floquet-ergodic phase. By contrast, I will show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases with spontaneously broken symmetries delineated by sharp transitions. Some of these are analogs of equilibrium states, while others are genuinely new to the Floquet setting.
The Kovtun-Son-Starinets conjecture that the ratio of the viscosity to the entropy density was bounded from below by fundamental constants has inspired over a decade of conjectures about fundamental bounds on the hydrodynamic and transport coefficients of strongly interacting quantum systems. I will present two complementary and (relatively) rigorous approaches to proving bounds on the transport coefficients of strongly interacting systems. Firstly, I will discuss lower bounds on the conductivities (and thus, diffusion constants) of inhomogeneous fluids, based around the principle that
Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics, respectively. In the last decade the study of quantum quenches revealed that these two concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure initial state maintains the system globally at zero entropy, at long time after the quench local properties are captured by an appropriate statistical ensemble with non zero thermodynamic entropy, which can be interpreted as the entanglement accumulated during the dynamics.