Dissimilarities of reduced density matrices and eigenstate thermalization hypothesis

Song He, Feng Li Lin, Jia ju Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


We calculate various quantities that characterize the dissimilarity of reduced density matrices for a short interval of length ℓ in a two-dimensional (2D) large central charge conformal field theory (CFT). These quantities include the Rényi entropy, entanglement entropy, relative entropy, Jensen-Shannon divergence, as well as the Schatten 2-norm and 4-norm. We adopt the method of operator product expansion of twist operators, and calculate the short interval expansion of these quantities up to order of ℓ9 for the contributions from the vacuum conformal family. The formal forms of these dissimilarity measures and the derived Fisher information metric from contributions of general operators are also given. As an application of the results, we use these dissimilarity measures to compare the excited and thermal states, and examine the eigenstate thermalization hypothesis (ETH) by showing how they behave in high temperature limit. This would help to understand how ETH in 2D CFT can be defined more precisely. We discuss the possibility that all the dissimilarity measures considered here vanish when comparing the reduced density matrices of an excited state and a generalized Gibbs ensemble thermal state. We also discuss ETH for a microcanonical ensemble thermal state in a 2D large central charge CFT, and find that it is approximately satisfied for a small subsystem and violated for a large subsystem.

Original languageEnglish
Article number73
JournalJournal of High Energy Physics
Issue number12
Publication statusPublished - 2017 Dec 1


  • AdS-CFT Correspondence
  • Conformal Field Theory
  • Field Theories in Lower Dimensions

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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