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Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems

Farrelly, Terry and Brandão, Fernando G. S. L. and Cramer, Marcus (2017) Thermalization and Return to Equilibrium on Finite Quantum Lattice Systems. Physical Review Letters, 118 (14). Art. No. 140601. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20170403-143421083

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Abstract

Thermal states are the bedrock of statistical physics. Nevertheless, when and how they actually arise in closed quantum systems is not fully understood. We consider this question for systems with local Hamiltonians on finite quantum lattices. In a first step, we show that states with exponentially decaying correlations equilibrate after a quantum quench. Then, we show that the equilibrium state is locally equivalent to a thermal state, provided that the free energy of the equilibrium state is sufficiently small and the thermal state has exponentially decaying correlations. As an application, we look at a related important question: When are thermal states stable against noise? In other words, if we locally disturb a closed quantum system in a thermal state, will it return to thermal equilibrium? We rigorously show that this occurs when the correlations in the thermal state are exponentially decaying. All our results come with finite-size bounds, which are crucial for the growing field of quantum thermodynamics and other physical applications.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.118.140601DOIArticle
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.140601PublisherArticle
ORCID:
AuthorORCID
Brandão, Fernando G. S. L.0000-0003-3866-9378
Additional Information:© 2017 American Physical Society. Received 7 November 2016; published 3 April 2017. The authors are grateful to Tobias Osborne and David Reeb for helpful discussions. This work was supported by the ERC Grants QFTCMPS (Quantum field theory, the variational principle, and continuous matrix product states) and SIQS (Simulators and Interfaces with Quantum Systems), by the cluster of excellence EXC201 Quantum Engineering and Space-Time Research, and by the DFG through Grant No. SFB 1227 Designte Quantenzustände der Materie (DQ-mat).
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
European Research Council (ERC)UNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)SFB 1227
Record Number:CaltechAUTHORS:20170403-143421083
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170403-143421083
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75651
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 Apr 2017 21:45
Last Modified:30 Jul 2018 15:21

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