Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session Y44: Thermalization and Chaos
11:30 AM–2:18 PM,
Friday, March 19, 2021
Sponsoring
Unit:
DCMP
Chair: Marko Znidaric, Univ of Ljubljana
Abstract: Y44.00006 : Spectral statistics in many-body quantum chaotic systems with symmetries
12:30 PM–12:42 PM
Live
Presenter:
Amos Chan
(Princeton University)
Authors:
Sanjay Moudgalya
(Walter Burke Institute for Theoretical Physics, California Institute of Technology)
Abhinav Prem
(Princeton University)
David A Huse
(Princeton University)
Amos Chan
(Princeton University)
We study the spectral statistics of spatially-extended many-body quantum systems with on-site Abelian symmetries or local constraints, focusing primarily on those with conserved dipole and higher moments. In the limit of large local Hilbert space dimension, we find that the spectral form factor of Floquet random circuits can be mapped exactly to a classical Markov circuit, and, at late times, is related to the partition function of a frustration-free Rokhsar-Kivelson (RK) type Hamiltonian. Through this mapping, we show that the inverse of the spectral gap of the RK-Hamiltonian lower bounds the Thouless time of the underlying circuit. For systems with conserved higher moments, we derive a field theory for the corresponding RK-Hamiltonian by proposing a generalized height field representation for the Hilbert space of the effective spin chain. Using the field theory formulation, we obtain the dispersion of the low-lying excitations of the RK-Hamiltonian in the continuum limit, which allows us to extract the Thouless time. In particular, we analytically argue that in a system of length L that conserves the m-th multipole moment, the Thouless time scales subdiffusively as L^(2m+2).
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