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Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis

He, S., Lin, F.-L., & Zhang, J.-j. (2017). Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis. Journal of high energy physics: JHEP, 2017(12): 073. doi:10.1007/JHEP12(2017)073.

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Genre: Journal Article

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1708.05090.pdf (Preprint), 832KB
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JHEP12(2017)073.pdf (Publisher version), 695KB
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Creators:
He, Song1, Author
Lin, Feng-Li, Author
Zhang, Jia-ju, Author
Affiliations:
1Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:102878

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Free keywords: High Energy Physics - Theory, hep-th, Condensed Matter, Statistical Mechanics, cond-mat.stat-mech,Quantum Physics, quant-ph
Abstract: We calculate various quantities that characterize the dissimilarity of reduced density matrices for a short interval of length $\ell$ in a two-dimensional (2D) large central charge conformal field theory (CFT). These quantities include the R\'enyi entropy, entanglement entropy, relative entropy, Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt the method of operator product expansion of twist operators, and calculate the short interval expansion of these quantities up to order of $\ell^9$ for the contributions from the vacuum conformal family. The formal forms of these dissimilarity measures and the derived Fisher information metric from contributions of general operators are also given. As an application of the results, we use these dissimilarity measures to compare the excited and thermal states, and examine the eigenstate thermalization hypothesis (ETH) by showing how they behave in high temperature limit. This would help to understand how ETH in 2D CFT can be defined more precisely. We discuss the possibility that all the dissimilarity measures considered here vanish when comparing the reduced density matrices of an excited state and a generalized Gibbs ensemble thermal state. We also discuss ETH for a microcanonical ensemble thermal state in a 2D large central charge CFT, and find that it is approximately satisfied for a small subsystem and violated for a large subsystem.

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Dates: 2017-08-1620172017
Publication Status: Published in print
Pages: 34 pages, 5 figures, see collection of complete results in the attached Mathematica notebook
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1708.05090
URI: http://arxiv.org/abs/1708.05090
DOI: 10.1007/JHEP12(2017)073
Degree: -

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### Source 1

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Title: Journal of high energy physics : JHEP
Source Genre: Journal
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Publ. Info: Bologna, Italy : Società italiana di fisica
Pages: - Volume / Issue: 2017 (12) Sequence Number: 073 Start / End Page: - Identifier: ISSN: 1126-6708
CoNE: http://pubman.mpdl.mpg.de/cone/journals/resource/111021927548002