This series consists of talks in the area of Condensed Matter.
Low-energy states of quantum spin liquids are thought to involve partons living in a gauge-field background. We study the spectrum of Majorana fermions of the Kitaev honeycomb model on spherical clusters. The gauge field endows the partons with half-integer orbital angular momenta. As a consequence, the multiplicities do not reflect the point-group symmetries of the cluster, but rather its projective symmetries, operations combining physical and gauge transformations. The projective symmetry group of the ground state is the double cover of the point group.
Topological phases of matter entail a prominent research theme, featuring
distinct characteristics that include protected metallic edge states and
the possibility of fractionalized excitations. With the advent of symmetry
protected topological (SPT) phases, many of these phenomena have
effectively become accessible in the form of readily available band
structures. Whereas the role of (anti-)unitary symmetries in such SPT
states has been thoroughly understood, the inclusion of lattice symmetries
provides for an active area of research.
Many strongly-correlated systems like high Tc cuprates and heavy fermions have interesting features going beyond quasi-particle description. While Sachdev-Ye-Kitaev(SYK) models are exactly solvable models that can provide a platform to study these physics. In this talk, I will discuss interesting features about the SYK models, including extensive zero temperature entropy and maximally chaos. I will also show some generalization of the SYK models and discuss physical insights from them.
Finite-size spectra and entanglement both characterize nonlocal physics of quantum systems, and are universal properties of a CFT. I discuss the energy spectrum of the Wilson-Fisher CFT on the torus in the \epsilon and 1/N expansions. I also consider a class of deconfined quantum critical points where the torus spectrum contains signatures of proximate Z2 topological order. Finally, I compute the entanglement entropy of the Wilson-Fisher and Gross-Neveu CFTs in the large N limit, where an exact mapping to free field entanglement is obtained. Comparison is made with numerics.
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.