Universality of quantum information in chaotic CFTs
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13130_2018_Article_7782.pdf
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Author(s)
Dymarsky, Anatoly
Lashkari, Nima
Liu, Hong
Date Issued
March 2018
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Lashkari, Nima, et al. “Universality of Quantum Information in Chaotic CFTs.” Journal of High Energy Physics, vol. 2018, no. 3, Mar. 2018. © The Authors
Version
Final published version
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
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP03(2018)070
