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Scientific article
Open access
English

Phases of scrambling in eigenstates

Published inSciPost physics, vol. 7, no. 1, 003
Publication date2019-07-04
First online date2019-07-04
Abstract

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.

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Keywords
  • Scaling: dimension
  • Field theory: conformal
  • N-point function: 6
  • Lyapunov exponent
  • Temperature
  • Oscillation
  • Holography
  • Monodromy
  • BTZ
Citation (ISO format)
ANOUS, Tarek, SONNER, Julian. Phases of scrambling in eigenstates. In: SciPost physics, 2019, vol. 7, n° 1, p. 003. doi: 10.21468/scipostphys.7.1.003
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Identifiers
ISSN of the journal2542-4653
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