Eigenstate thermalization hypothesis in conformal field theory

Nima Lashkari, Anatoly Dymarsky, Hong Liu

Research output: Contribution to journalArticlepeer-review

76 Scopus citations


We investigate the eigenstate thermalization hypothesis (ETH) in d + 1 dimensional conformal field theories by studying the reduced density matrices in energy eigenstates. We show that if the local probes of the finitely excited primary eigenstates satisfy ETH, then any finite energy observable with support on a subsystem of finite size satisfies ETH. In two dimensions, we discover that if ETH holds locally, the finite size reduced density matrix of states created by heavy primary operators is well-approximated by a projection to the Virasoro identity block.

Original languageEnglish
Article number033101
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number3
StatePublished - Mar 8 2018

Bibliographical note

Funding Information:
We would like to thank Ahmed Almheiri, John Cardy, Thomas Faulkner, Liam Fitzpatrick, Daniel Harlow, Thomas Hartman, Tarun Grover, Mark Srednicki and Sasha Zhiboedov for valuable discussions. The research of NL is supported in part by funds provided by MIT-Skoltech Initiative. This paper has the preprint number Technical Report MIT-CTP/4841. This work is supported by the Oce of High Energy Physics of US Department of Energy under grant Contract Number DE-SC0012567.

Publisher Copyright:
© 2018 IOP Publishing Ltd and SISSA Medialab srl.


  • conformal field theory
  • entanglement in extended quantum systems
  • quantum thermalization

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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