This series consists of talks in the area of Condensed Matter.
In crystals, quantum electrons can be spatially distributed in a way that the bulk solid supports macroscopic electric multipole moments, which are deeply
related with emergence of topology insulators in condensed matter systems. However, unlike the classical electric multipoles in open space,
defining electric multipoles in crystals is a non-trivial task. So far, only the dipolar moment, namely polarization, has been successfully defined and served as a classic example of topological insulators.
This year there appear several amazing experiments in the graphene moire superlattices. In this talk I will focus on the ABC trilayer graphene/h-BN system. Mott-like insulators at 1/4 and 1/2 of the valence band have already been reported by Feng Wang’s group at Berkeley. The sample is dual gated on top and bottom with voltage V_t and V_b. V_t+V_b controls the density of electrons. Interestingly we find that the displacement field D=V_t-V_b can control both the topology and the bandwidth of the valence band.
Applying a chemical potential bias to a conductor drives the system out of equilibrium into a current carrying non-equilibrium state. This current flow is associated with entropy production in the leads, but it remains poorly understood under what conditions the system is driven to local equilibrium by this process. We investigate this problem using two toy models for coherent quantum transport of diffusive fermions: Anderson models in the conducting phase and a class of random quantum circuits acting on a chain of qubits, which exactly maps to an interacting fermion problem.
Despite much theoretical effort, there is no complete theory of the “strange” metal phase of the high temperature
superconductors, and its linear-in-temperature resistivity. This phase is believed to be a strongly-interacting metallic
phase of matter without fermionic quasiparticles, and is virtually impossible to model accurately using traditional
perturbative field-theoretic techniques. Recently, progress has been made using large-N techniques based on the
Three dimensional fracton phases are new type of phases featuring exotic excitations called fractons. They are gapped point-like excitations constrained to move in sub-dimensional space. In this talk, I will present the gapped fracton topological order discovered in exact solvable models and gapless fracton phase described by U(1) symmetric tensor gauge theories. Their relation with ordinary topological ordered phase would be discussed in detail.
Searching for a proper set of order parameters which distinguishes different phases of matter sits in the heart of condensed matter physics. In this talk, I discuss topological invariants as (non-local) order parameters for symmetry protected topological (SPT) phases of fermions in the presence of time-reversal symmetry.
Classical chaotic systems exhibit exponential divergence of initially infinitesimally close trajectories, which is characterized by the Lyapunov exponent. This sensitivity to initial conditions is popularly known as the "butterfly effect." Of great recent interest has been to understand how/if the butterfly effect and Lyapunov exponents generalize to quantum mechanics, where the notion of a trajectory does not exist.
Entanglement spectrum (ES) contains more information than the entanglement entropy, a single number. For highly excited states, this can be quantified by the ES statistics, i.e. the distribution of the ratio of adjacent gaps in the ES. I will first present examples in both random unitary circuits and Hamiltonian systems, where the ES signals whether a time-evolved state (even if maximally entangled) can be efficiently disentangled without precise knowledge of the time evolution operator.
I give an overview of work with Aasen and Mong on topologically invariant defects in two-dimensional classical lattice models, quantum spin chains and tensor networks. We show how to find defects that satisfy commutation relations guaranteeing the partition function depends only on their topological properties. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. These lattice topological defects have a variety of useful applications.
Large deviation theory gives a general framework for studying nonequilibrium systems which in many ways parallels equilibrium thermodynamics. In transport, according to the large deviation principle, the distribution of rare fluctuations of the total transfer (of charge, energy, etc.) between two baths take a special form encoded by the large deviation function, which plays the role of a free energy. Its Legendre transform is the scaled cumulant generating function (SCGF).