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  Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT

He, S., Lin, F.-L., & Zhang, J.-j. (in press). Subsystem eigenstate thermalization hypothesis for entanglement entropy in CFT.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-0A30-B Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-DAFF-2
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1703.08724.pdf (Preprint), 659KB
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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, Condensed Matter, Strongly Correlated Electrons, cond-mat.str-el,Quantum Physics, quant-ph
 Abstract: In order to investigate subsystem eigenstate thermalization hypothesis (ETH) for two-dimensional large central charge conformal field theory, we evaluate the single-interval R\'enyi entropy and entanglement entropy for a heavy primary state in short interval expansion. We verify the results of R\'enyi entropy by three different replica methods. We find nontrivial results at the eighth order of short interval expansion, which include an infinite number of higher order terms in the large central charge expansion. We then evaluate the relative entropy of the reduced density matrices to measure the difference between the heavy primary state and thermal state, and find that the aforementioned nontrivial eighth order results make the relative entropy unsuppressed in the large central charge limit. By Fannes-Audenaert inequality, these results yield a lower bound on trace distance of the excited state and thermal state reduced density matrices, which is crucial in checking the validity of subsystem ETH. We find that whether the subsystem ETH is violated depends on how the effective dimension of the reduced density matrix scales with the large central charge. If the effective dimension is strictly infinite, then it yields no useful information for checking the validity of subsystem ETH. If the effective dimension scales exponentially with the large central charge, the trace distance is at most power suppressed, and subsystem ETH would be violated, while the local ETH remains intact. As a byproduct we also calculate the relative entropy and distance to measure the difference between the reduced density matrices of two different heavy primary states.

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 Dates: 2017-03-252017-03-292017
 Publication Status: Accepted / In Press
 Pages: 26 pages, 4 figures;v2 change author list
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1703.08724
URI: http://arxiv.org/abs/1703.08724
 Degree: -

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