Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
131 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Spectral statistics in constrained many-body quantum chaotic systems (2009.11863v2)

Published 24 Sep 2020 in cond-mat.stat-mech, cond-mat.str-el, and quant-ph

Abstract: 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 $K(t)$ 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 $t_{\mathrm{Th}}$ 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 $t_{\mathrm{Th}}$. In particular, we analytically argue that in a system of length $L$ that conserves the $m{th}$ multipole moment, $t_{\mathrm{Th}}$ scales subdiffusively as $L{2(m+1)}$. We also show that our formalism directly generalizes to higher dimensional circuits, and that in systems that conserve any component of the $m{th}$ multipole moment, $t_{\mathrm{Th}}$ has the same scaling with the linear size of the system. Our work therefore provides a general approach for studying spectral statistics in constrained many-body chaotic systems.

Summary

We haven't generated a summary for this paper yet.