This series consists of talks in the area of Quantum Matter.
The construction of soluble lattice toy models is an important theoretical approach in the study of strongly interacting topological phases of matter. On the other hand, the primary experimental probe to such systems is via electromagnetic response. Somewhat unsatisfactorily, the current systematic construction of the lattice toy models focuses on braiding statistics and does not admit coupling to an electromagnetic background. Thus there is a mismatch between our theoretical approach and experimental probe.
Experiments with ultracold fermionic gases are thriving and continue to provide us with valuable insights into fundamental aspects of physics. A special system of interest is the so-called unitary Fermi gas (UFG) situated right in the "middle" of the crossover between Bardeen-Cooper-Schrieffer superfluidity and Bose-Einstein condensation. However, the theoretical treatment of these gases is highly challenging due to the absence of a small expansion parameter as well as the appearance of the infamous sign problem in the presence of, e.g., finite spin polarizations.
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.