Group Meetings Schedule 2024
Jan 29, Sayan Choudhury, Monday 9:00 am Pitt time (10:00 PM Beijing time)
Feb 7, Simon Shi, Wednesday 8:30 pm Pitt time (Thu, Feb 8, 9:30 AM Beijing time)
Title: Magic of Topological Moiré Bands — Fractional and Integer Quantum Anomalous Hall Effects
Abstract: Moiré superlattices are exciting platforms to study interaction-driven exotic phases of matter. I will mainly present my recent doctoral work motivated by the observation of fractional quantum anomalous Hall effect in twisted homobilayer transitional metal dichalcogenides. An adiabatic approximation, which maps the moiré bands to a hole gas in a nonuniform periodic pseudo-magnetic field and a periodic potential, has been proposed to explain the occurrence of the flat band and ideal quantum geometry. We show that the adiabatic approximation is accurate under realistic conditions, and that the ideal quantum geometry arises from a partial Aharonov-Casher cancellation between the magnetic field and the potential. Interestingly, higher-shell Fourier components of the residual potential do not strongly violate the ideal quantum geometry though they do change wave functions. Next, I will briefly present my earlier work on twisted bilayer graphene aligned with hexagonal boron nitride (hBN), in which we propose that the appearance or absence of quantum anomalous Hall effect depends on the commensurability between the two moiré patterns, one between the two graphene layers and the other between the hBN and its adjacent graphene layer.
Feb 14, Nikolay Yegovtsev, Wednesday 8:30 pm Pitt time (Thu, Feb 15, 9:30 AM Beijing time)
Title: Exact results for heavy unitary Bose polarons
Abstract: We consider the problem of unitary Bose polarons, i.e., impurities interacting via a potential with infinite scattering length with a bath of weakly interacting bosons. We show that this problem can be solved analytically in two regimes, where the impurity-boson interaction potential has a range both much smaller and larger than the healing length of the bath. We provide various expressions for the energy and other quasiparticle properties of the polaron in those regimes. Furthermore, we perform numerically exact Diffusion Monte Carlo calculations and we demonstrate that the simple Gross-Pitaevskii theory provides a remarkably accurate description of heavy unitary Bose polarons throughout the whole experimentally relevant range of gas densities.
Feb 21, Anupam Mitra, Wednesday 8:30 pm Pitt time (Thu, Feb 22, 9:30 AM Beijing time)
Title: Entanglement and Classical Tractability in the Critical Phenomena in Quench Dynamics of 1D Ising Models
Abstract: Progress towards building scalable quantum information processing systems has facilitated the ability to study the dynamics of interacting quantum many-body systems. In fact, analog quantum simulators using trapped ions, neutral atoms, solid state systems and many others are routinely used to study these dynamics, often in regimes that are not amenable to precise classical simulation through exact diagonalization. In this talk, I report classical simulation of critical phenomena in the quench dynamics of one-dimensional transverse field Ising models (TFIMs) using highly truncated matrix product states (MPS). I show that even when high-fidelity simulation of the full many-body state is intractable due to exponential scaling with system size, macroscopic quantities like order parameters, the critical point and critical exponents of a dynamical quantum phase transition can be efficiently simulated. I also discuss the classical simulation of infinite-time correlation length of the integrable nearest-neighbor TFIM when quenched to the critical point. In this scenario, the quantities of interest are accessible from short-time dynamics after a quantum quench when many-body entanglement is small, yet they become intractable at later times due to volume-law growth of entanglement. I also discuss the tractability of simulation using truncated MPS based on quantum chaos and equilibration in the models, showing evidence for a counterintuitive inverse relationship, whereby local expectation values are most easily approximated for chaotic systems whose exact many-body state is most intractable.
Feb 28, Sandeep Joy, Wednesday 8:30 pm Pitt time (Thu, Feb 29, 9:30 AM Beijing time)
Title: The story of Wigner crystallization in Bernal bilayer graphene
Abstract: In Bernal bilayer graphene (BBG), a perpendicular displacement field flattens the bottom of the conduction band and thereby facilitates the formation of strongly-correlated electron states at low electron density. Here, we focus on the Wigner crystal (WC) state, which appears in a certain regime of sufficiently large displacement field, low electron density, and low temperature. We first consider a model of BBG without trigonal warping, and we show theoretically that Berry curvature leads to a new kind of WC state in which the electrons acquire a spontaneous orbital magnetization when the displacement field exceeds a critical value. We then consider the effects of trigonal warping in BBG, and we show that they lead to an unusual ``doubly re-entrant" behavior of the WC phase as a function of density. The rotational symmetry breaking associated with trigonal warping leads to a nontrivial ``minivalley order" in the WC state, which changes abruptly at a critical value of displacement field. In both cases, we estimate the phase boundary of the WC state in terms of density, displacement field, and temperature.
Ref: arXiv.2310.07751
March 6: Zenan Liu, Wednesday 8:30 pm Pitt time (Thu, Mar 7, 9:30 AM Beijing time)
Title: Quantum Monte Carlo study on 2d Affleck-Kennedy-Lieb-Tasaki model
Abstract: Affleck-Kennedy-Lieb-Tasaki (AKLT) phase is a symmetry-protected topological (SPT) phase, which can be efficiently constructed in the S=1/2 Heisenberg model on the square-octagon lattice, dubbed as 2d AKLT model. In this talk, I will introduce the Quantum Monte Carlo (QMC) study on the physics of 2d AKLT model. Firstly, I will show how I utilize QMC to reveal the dynamical excitation spectrum of bulk and edge spin. The spin excitation helps us understand the physical properties of SPT phase. Next, I will talk about the newly-proposed QMC method for entanglement spectrum. Taking the 2d AKLT model as an example, I explore the relationship between entanglement spectrum and energy spectrum for the gapless and gapped boundary cases. Finally, I will show the non- local operator-disorder operator can be used to detect the boundary state and boundary criticality, which can reveal the complex conformal field theory information at boundary criticality.
Daylight Savings Time Starts
Mar 13, Sanjib Kumar Das, Wednesday 9:00 pm Pitt time (Thu, Mar 14, 9:00 AM Beijing time)
Title: Quantized electrical, thermal and spin responses of two-dimensional disordered (non-)Hermitian topological insulators and superconductors
Abstract:
Altland-Zirnbauer topological classification of quantum phases of matter shows that there are five topologically nontrivial classes in every spatial dimension. Particularly in two spatial dimensions, there are two insulating (namely, quantum Hall and quantum spin Hall insulators) and three superconducting (namely, 𝑝+𝑖𝑝, 𝑑+𝑖𝑑 and 𝑝𝑝𝑚𝑖𝑝 pairings) AZ phases. The bulk topological invariant of these phases of matter manifests quantized electrical and thermal responses that can be experimentally measured in multi-terminal Hall bar geometries. In this work, I will demonstrate such quantized electric and thermal responses of disordered topological insulators and superconductors, computed within the scattering matrix formalism using the software package Kwant. Furthermore, I will show that in the weak disorder regime such quantized responses are robust, while they vanish smoothly for strong disorder. Finally, I will show that the jurisdiction of these outcomes extends to the landscape of non-Hermitian dirty two-dimensional topological insulators and superconductors.
Apr 3, Hongyu Wang, Wednesday 9:00 am Pitt time (Thu, Apr 4, 9:00 AM Beijing time)
Apr 24, Bao-Zong Wang, Wednesday 9:00 am Pitt time (Thu, Apr 25, 9:00 AM Beijing time)
May 1, Haoran Sun, Wednesday 9:00 am Pitt time (Thu, May 2, 9:00 AM Beijing time)
May 15, Xin-Chi Zhou, Wednesday 9:00 am Pitt time (Thu, May 16, 9:00 AM Beijing time)
Summar Schedule Starts
