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Universality of quantum information in chaotic CFTs

  • Nima LashkariEmail author
  • Anatoly Dymarsky
  • Hong Liu
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Conformal Field Theory Integrable Hierarchies Thermal Field Theory 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeU.S.A.
  2. 2.Department of Physics and AstronomyUniversity of KentuckyLexingtonU.S.A.
  3. 3.Skolkovo Institute of Science and Technology, Skolkovo Innovation CenterMoscowRussia

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