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Phases of scrambling in eigenstates

by Tarek Anous, Julian Sonner

Submission summary

As Contributors: Tarek Anous · Julian Sonner
Arxiv Link: (pdf)
Date accepted: 2019-06-18
Date submitted: 2019-06-13 02:00
Submitted by: Anous, Tarek
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • High-Energy Physics - Theory
Approach: Theoretical


We use the monodromy method to compute expectation values of an arbitrary number of light operators in finitely excited ("heavy") eigenstates of holographic 2D CFT. For eigenstates with scaling dimensions above the BTZ threshold, these behave thermally up to small corrections, with an effective temperature determined by the heavy state. Below the threshold we find oscillatory and not decaying behavior. As an application of these results we compute the expectation of the out-of-time order arrangement of four light operators in a heavy eigenstate, i.e. a six-point function. Above the threshold we find maximally scrambling behavior with Lyapunov exponent $2\pi T_{\rm eff}$. Below threshold we find that the eigenstate OTOC shows persistent harmonic oscillations.

Ontology / Topics

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Conformal field theory (CFT) Holography Lyapunov exponents

Published as SciPost Phys. 7, 003 (2019)

Author comments upon resubmission

Dear Editor,

We have addressed the referee’s comments and fixed the two typos they pointed out. We have also seized the opportunity to correct two further minor typos. See list of changes.

Reply to referee:

We would like to thank the referee for their careful reading and insightful report. We reply to their comment as follows:

The referee raises the important point of the validity of the assumption of identity block domination and whether a further hierarchy among the light operators is necessary. Such an additional hierarchy is not necessary for our result to hold, one merely needs to assume that the total contribution to the semiclassical stress tensor coming from the aggregate effect of the Q operators is $O(\varepsilon c)$ in the notation of our paper.

As an example we have shown how to extract the Lyapunov exponent from a six-point function between two heavy and four light operators, with no additional hierarchy between the latter. Nevertheless it would be interesting to investigate if further mileage can be gained from making the additional assumption of such a hierarchy.

List of changes

igure 2: replaced erroneous ‘=' sign with the word ‘operators’.
Page 8, below Eq. (3.10): fixed an incorrect subscript on the matrix $M$.
Top of page 14: we fixed the sentence structure, as pointed out by the referee.
Page 17: minor typo fixed (“does not decays” replaced by “does not decay”).

Submission & Refereeing History

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Resubmission 1903.03143v3 on 13 June 2019

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