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Title: Universality of quantum information in chaotic CFTs

Abstract

We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.

Authors:
 [1];  [2];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  2. Univ. of Kentucky, Lexington, KY (United States); Skolkovo Inst. of Science and Technology, Moscow, (Russia)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1498701
Grant/Contract Number:  
SC0012567
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 3; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Theory; Integrable Hierarchies; Thermal Field Theory

Citation Formats

Lashkari, Nima, Dymarsky, Anatoly, and Liu, Hong. Universality of quantum information in chaotic CFTs. United States: N. p., 2018. Web. doi:10.1007/jhep03(2018)070.
Lashkari, Nima, Dymarsky, Anatoly, & Liu, Hong. Universality of quantum information in chaotic CFTs. United States. doi:10.1007/jhep03(2018)070.
Lashkari, Nima, Dymarsky, Anatoly, and Liu, Hong. Mon . "Universality of quantum information in chaotic CFTs". United States. doi:10.1007/jhep03(2018)070. https://www.osti.gov/servlets/purl/1498701.
@article{osti_1498701,
title = {Universality of quantum information in chaotic CFTs},
author = {Lashkari, Nima and Dymarsky, Anatoly and Liu, Hong},
abstractNote = {We study the Eigenstate Thermalization Hypothesis (ETH) in chaotic conformal field theories (CFTs) of arbitrary dimensions. Assuming local ETH, we compute the reduced density matrix of a ball-shaped subsystem of finite size in the infinite volume limit when the full system is an energy eigenstate. This reduced density matrix is close in trace distance to a density matrix, to which we refer as the ETH density matrix, that is independent of all the details of an eigenstate except its energy and charges under global symmetries. In two dimensions, the ETH density matrix is universal for all theories with the same value of central charge. We argue that the ETH density matrix is close in trace distance to the reduced density matrix of the (micro)canonical ensemble. We support the argument in higher dimensions by comparing the Von Neumann entropy of the ETH density matrix with the entropy of a black hole in holographic systems in the low temperature limit. Finally, we generalize our analysis to the coherent states with energy density that varies slowly in space, and show that locally such states are well described by the ETH density matrix.},
doi = {10.1007/jhep03(2018)070},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2018,
place = {United States},
year = {2018},
month = {3}
}

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Cited by: 19 works
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    • Guo, Wu-zhong; Lin, Feng-Li; Zhang, Jiaju
    • Journal of High Energy Physics, Vol. 2019, Issue 8
    • DOI: 10.1007/jhep08(2019)010