Off-diagonal observable elements from random matrix theory: Distributions, fluctuations, and eigenstate thermalization

26 pags., 9 figs., 2 apps. -- Open Access funded by Creative Commons Atribution Licence 3.0

Bibliographic Details
Authors: Porras, Diego, Nation, Charlie
Format: article
Status:Published version
Publication Date:2018
Country:España
Institution:Consejo Superior de Investigaciones Científicas (CSIC)
Repository:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/202036
Online Access:http://hdl.handle.net/10261/202036
Access Level:Open access
Keyword:Eigenstate thermalization hypothesis
Quantum non-equilibrium physics
Quantum thermalization
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spelling Off-diagonal observable elements from random matrix theory: Distributions, fluctuations, and eigenstate thermalizationPorras, DiegoNation, CharlieEigenstate thermalization hypothesisQuantum non-equilibrium physicsQuantum thermalization26 pags., 9 figs., 2 apps. -- Open Access funded by Creative Commons Atribution Licence 3.0We derive the eigenstate thermalization hypothesis(ETH)from a random matrix Hamiltonian by extending the model introduced by Deutsch (1991 Phys. Rev. A 43 2046). We approximate the coupling between a subsystem and a many-body environment by means of a random Gaussian matrix. We show that a common assumption in the analysis of quantum chaotic systems, namely the treatment of eigenstates as independent random vectors, leads to inconsistent results. However, a consistent approach to the ETH can be developed by introducing an interaction between random wave-functions that arises as a result of the orthonormality condition. This approach leads to a consistent form for off-diagonal matrix elements of observables. From there we obtain the scaling of time-averaged fluctuations of generic observables with system size for which we calculate an analytic form in terms of the inverse participation ratio. The analytic results are compared to exact diagonalizations of a quantum spin chain for different physical observables in multiple parameter regimes.We acknowledge funding by the People Programme (Marie Curie Actions) of the EUs Seventh Framework Programme under REA Grant Agreement No. PCIG14-GA-2013-630955 and EPSRC grant number EP/M508172/1.Institute of Physics PublishingEuropean CommissionSCOAPEngineering and Physical Sciences Research Council (UK)2020202020182020info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/202036reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/EC/FP7/630955http://dx.doi.org/10.1088/1367-2630/aae28fnoinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/2020362026-05-22T06:33:51Z
dc.title.none.fl_str_mv Off-diagonal observable elements from random matrix theory: Distributions, fluctuations, and eigenstate thermalization
title Off-diagonal observable elements from random matrix theory: Distributions, fluctuations, and eigenstate thermalization
spellingShingle Off-diagonal observable elements from random matrix theory: Distributions, fluctuations, and eigenstate thermalization
Porras, Diego
Eigenstate thermalization hypothesis
Quantum non-equilibrium physics
Quantum thermalization
title_short Off-diagonal observable elements from random matrix theory: Distributions, fluctuations, and eigenstate thermalization
title_full Off-diagonal observable elements from random matrix theory: Distributions, fluctuations, and eigenstate thermalization
title_fullStr Off-diagonal observable elements from random matrix theory: Distributions, fluctuations, and eigenstate thermalization
title_full_unstemmed Off-diagonal observable elements from random matrix theory: Distributions, fluctuations, and eigenstate thermalization
title_sort Off-diagonal observable elements from random matrix theory: Distributions, fluctuations, and eigenstate thermalization
dc.creator.none.fl_str_mv Porras, Diego
Nation, Charlie
author Porras, Diego
author_facet Porras, Diego
Nation, Charlie
author_role author
author2 Nation, Charlie
author2_role author
dc.contributor.none.fl_str_mv European Commission
SCOAP
Engineering and Physical Sciences Research Council (UK)
dc.subject.none.fl_str_mv Eigenstate thermalization hypothesis
Quantum non-equilibrium physics
Quantum thermalization
topic Eigenstate thermalization hypothesis
Quantum non-equilibrium physics
Quantum thermalization
description 26 pags., 9 figs., 2 apps. -- Open Access funded by Creative Commons Atribution Licence 3.0
publishDate 2018
dc.date.none.fl_str_mv 2018
2020
2020
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/202036
url http://hdl.handle.net/10261/202036
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/EC/FP7/630955
http://dx.doi.org/10.1088/1367-2630/aae28f
no
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Institute of Physics Publishing
publisher.none.fl_str_mv Institute of Physics Publishing
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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