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Noncommuting conserved charges in quantum many-body thermalization

Yunger Halpern, Nicole and Beverland, Michael E. and Kalev, Amir (2020) Noncommuting conserved charges in quantum many-body thermalization. Physical Review E, 101 (4). Art. No. 042117. ISSN 2470-0045. https://resolver.caltech.edu/CaltechAUTHORS:20200103-094850055

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Abstract

In statistical mechanics, a small system exchanges conserved quantities—heat, particles, electric charge, etc.—with a bath. The small system thermalizes to the canonical ensemble or the grand canonical ensemble, etc., depending on the quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed “the non-Abelian thermal state (NATS).” We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to near the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevE.101.042117DOIArticle
https://arxiv.org/abs/1906.09227arXivDiscussion Paper
ORCID:
AuthorORCID
Yunger Halpern, Nicole0000-0001-8670-6212
Alternate Title:Equilibration to the non-Abelian thermal state in quantum many-body physics
Additional Information:© 2020 American Physical Society. Received 30 June 2019; revised manuscript received 13 March 2020; accepted 17 March 2020; published 15 April 2020. The authors are grateful to many people for illuminating discussions: Á. M. Alhambra, Y. Alhassid, A. Browaeys, L. Carr, V. Dunjko, M. Endres, P. Faist, M. Greiner, V. Khemani, J. Léonard, Sw. Lloyd, M. Lukin, N. Lupu-Gladstein, M. Olshanyi, J. Oppenheim, A. P. Orioli, A. M. Rey, M. Rigol, V. Vuletic, A. Winter, and M. Woods. N.Y.H. is grateful for funding from the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (NSF Grant No. PHY-1125565) with support from the Gordon and Betty Moore Foundation (Grant No. GBMF-2644); for an NSF grant for the Institute for Theoretical Atomic, Molecular, and Optical Physics at Harvard University and the Smithsonian Astrophysical Observatory; and for hospitality at the KITP (supported by NSF Grant No. NSF PHY-1748958), during its 2018 “Quantum Thermodynamics” conference. A.K. acknowledges support from the U.S. Department of Defense.
Group:UNSPECIFIED, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFPHY-1125565
Gordon and Betty Moore FoundationGBMF-2644
Harvard UniversityUNSPECIFIED
Smithsonian Astrophysical ObservatoryUNSPECIFIED
NSFPHY-1748958
Department of DefenseUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20200103-094850055
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200103-094850055
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100489
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Jan 2020 03:44
Last Modified:04 Jun 2020 10:14

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