Signature of quantum chaos in operator entanglement in 2d CFTs

Laimei Nie, Masahiro Nozaki, Shinsei Ryu, Mao Tian Tan

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We study operator entanglement measures of the unitary evolution operators of (1 + 1)-dimensional conformal field theories (CFTs), aiming to uncover their scrambling and chaotic behaviors. In particular, we compute the bi-partite and tri-partite mutual information for various configurations of input and output subsystems, and as a function of time. We contrast three different CFTs: the free fermion theory, compactified free boson theory at various radii, and CFTs with holographic dual. We find that the bi-partite mutual information exhibits distinct behaviors for these different CFTs, reflecting the different information scrambling capabilities of these unitary operators; while a quasi-particle picture can describe the case of the free fermion and free boson CFTs well, it completely fails for the case of holographic CFTs. Similarly, the tri-partite mutual information also distinguishes the unitary evolution operators of different CFTs. In particular, its late-time behaviors, when the output subsystems are semi-infinite, are quite distinct for these theories. We speculate that for holographic theories the late-time saturation value of the tri-partite mutual information takes the largest possible negative value and saturates the lower bound among quantum field theories.

Original languageEnglish (US)
Article number093107
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number9
StatePublished - 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

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


  • AdS/CFT correspondence
  • Conformal field theory
  • Entanglement entropies
  • Quantum chaos


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