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The coupled wire construction is a powerful method for studying exotic quantum phases of matter. In this talk I will discuss some recent work in which this technique was used to realize new types of 3D compressible quantum phases. These phases possess a U(1) charge conservation symmetry that is weakly broken by rigid string or membrane-like order parameters. No local order parameter is present and the emergent quasiparticles have restricted mobility. I will discuss the unusual symmetry breaking mechanism and its connection to the compressibility. For a particular class of models I will also describe an effective low energy theory given by coupled layers Maxwell-Chern-Simons theories.

Zoom Link: https://pitp.zoom.us/j/95372524441?pwd=UTlVTTZlSmFRK0FmVE5pTHhDRThwdz09

The charge resistivity/conductivity can take universal values in various scenarios of two-dimensional condensed matter systems. Well-known examples of universal resistivity include 2+1d quantum critical points, (fractional) quantum Hall effects, the criterion of two-dimensional “bad metal”, and the universal resistivity jump predicted at the interaction-driven metal-insulator transition. We construct examples of two-dimensional metallic states with the following exotic behaviors: (1) at low temperature this state is a “bad metal” whose resistivity can be much larger than the Mott-Ioffe-Regel limit; (2) while increasing temperature T the resistivity ρ(T) crosses over from a bad metal at low T to a good metal at intermediate T; (3) at low temperature the metallic state has a large Lorenz number, which strongly violates the Wiedemann-Franz law; (4) the state also has a large thermopower (Seebeck coefficient). Motivated by the recent experiment in transition metal dichalcogenides, an exotic interaction-driven metal-insulator transition will also be constructed. The universal resistivity jump at this transition far exceeds what was proposed in previous theory.

Zoom Link: https://pitp.zoom.us/j/93625929658?pwd=Y284ZTZpWFM1RnduSmhXdDZBRjgyQT09

When an interacting quantum many-body system is cooled down to its ground state, there can be discrete "topological invariants" that characterize the properties of such ground states. This leads to the concept of "topological phases of matter" distinguished by these topological invariants. Experimental manifestations of these topological phases of matter include the integer and fractional quantum Hall effect, as well as topological insulators.

In this talk, after a general overview of topological phases of matter, I will explain how to define topological invariants that are specific to the ground states of regular crystals, i.e. systems that are periodic in space. I will discuss the physical manifestations of the resulting "crystalline topological phases", including implications for the properties of crystalline defects such as dislocations and disclinations. Then, I will explain how these ideas can be generalized to quasicrystals, which are a different class of materials that have long-range spatial order without exact periodicity. These ideas ultimately lead to a general classification principle for crystalline and quasicrystalline topological phases of matter.

I will first give a brief overview of my research in the field of out-of-equilibrium quantum many-
body physics, ranging from the theory of many-body localization, to the recent application of Tensor

Processing Units for accelerating simulations of quantum dynamics. I’ll then focus on (1) the

experimental observation and theoretical explanation of subdiffusive dynamics in a “tilted” Fermi-
Hubbard system [PRX 10, 011042 (2020)], and (2) a “freezing” phase transition between weak and

strong ergodicity breaking in systems with particles that are immobile by themselves, but undergo
coordinated pair hopping [PRB 101, 214205 (2020)]. These topics contain the common thread of
either an emergent or microscopic conservation of the dipole moment (center of mass of the particle
distribution), and I will provide simple pictures for how this leads to the subdiffusion and ergodicity
breaking.

In thermal equilibrium, 1d bosonic systems (e.g. spin- or qubit- chains) cannot support intrinsically topological phases without symmetry protection. For example, the edge states of the Haldane spin chain are fragile to magnetic fields, in contrast to the absolutely stable Majorana edge states of a topological superconducting wire of fermionic electrons. This fragility is a serious drawback to harnessing topological edge states as protected quantum memories in existing AMO and qubit platforms for quantum simulation and information processing. In this talk, I will present evidence for a non-equilibrium topological phase of quasiperiodically-driven trapped ion chains, that exhibits topological edge states that are protected purely by emergent dynamical symmetries that cannot be broken by microscopic perturbations. This represents both the first experimental realization of a non-equilibrium quantum phase, and the first example of a 1d bosonic topological phase that does not rely on symmetry-protection.

Conformal field theories (CFTs) are ubiquitous in theoretical physics as fixed points of renormalization, descriptions of critical systems and more. In these theories the conformal symmetry is a powerful tool in the computation of correlation functions, especially in 2 dimensions where the conformal algebra is infinite. Discretization of field theories is another powerful tool, where the theory on the lattice is both mathematically well-defined and easy to put on a computer. In this talk I will outline how these are combined using a discrete version of the 2d conformal algebra that acts in lattice models. I will also discuss recent work on convergence of this discretization, as well as on applications to non-unitary CFTs that appear in descriptions of problems of interest in condensed matter physics such as polymers, percolation and disordered systems.

Zoom Link: https://pitp.zoom.us/j/95048143778?pwd=N1hhVHlsZThVYzBWTy9CNlBTUHIydz09