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Spectral statistics in constrained many-body quantum chaotic systems

Moudgalya, Sanjay and Prem, Abhinav and Huse, David A. and Chan, Amos (2021) Spectral statistics in constrained many-body quantum chaotic systems. Physical Review Research, 3 (2). Art. No. 023176. ISSN 2643-1564. doi:10.1103/physrevresearch.3.023176.

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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_(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_(Th). In particular, we analytically argue that in a system of length L that conserves the mth multipole moment, t_(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 mth multipole moment, t_(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.

Item Type:Article
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URLURL TypeDescription Paper
Prem, Abhinav0000-0003-4438-7107
Huse, David A.0000-0003-1008-5178
Additional Information:© 2021 The Author(s). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. (Received 4 January 2021; revised 8 April 2021; accepted 12 April 2021; published 4 June 2021) We are particularly grateful to Shivaji Sondhi for enlightening discussions. We also acknowledge useful conversations with Nathan Benjamin, John Chalker, Andrea De Luca, Alan Morningstar, and Pablo Sala. A.P. was supported in part with funding from the Defense Advanced Research Projects Agency (DARPA) via the DRINQS program. The views, opinions and/or findings expressed are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. A.C. is supported in part by the Croucher foundation. A.P. and A.C. are supported by fellowships at the PCTS at Princeton University. D.A.H. is supported in part by DOE grant DE-SC0016244. This publication was supported in part by the Princeton University Library Open Access Fund.
Group:Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Croucher FoundationUNSPECIFIED
Princeton UniversityUNSPECIFIED
Department of Energy (DOE)DE-SC0016244
Issue or Number:2
Record Number:CaltechAUTHORS:20210607-115052641
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109411
Deposited By: George Porter
Deposited On:07 Jun 2021 21:28
Last Modified:16 Nov 2021 19:35

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