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Temporal fluctuations of correlators in integrable and chaotic quantum systems

by Talía L. M. Lezama, Yevgeny Bar Lev, Lea F. Santos

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Submission summary

Authors (as registered SciPost users): Yevgeny Bar Lev · Talía L. M. Lezama
Submission information
Preprint Link: scipost_202311_00029v1  (pdf)
Date accepted: 2023-11-30
Date submitted: 2023-11-17 19:20
Submitted by: L. M. Lezama, Talía
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


We provide bounds on temporal fluctuations around the infinite-time average of out-of-time-ordered and time-ordered correlators of many-body quantum systems without energy gap degeneracies. For physical initial states, our bounds predict the exponential decay of the temporal fluctuations as a function of the system size. We numerically verify this prediction for chaotic and interacting integrable spin-1/2 chains, which satisfy the assumption of our bounds. On the other hand, we show analytically and numerically that for the XX model, which is a noninteracting system with gap degeneracies, the temporal fluctuations decay polynomially with system size for operators that are local in the fermion representation and decrease exponentially in the system size for non-local operators. Our results demonstrate that the decay of the temporal fluctuations of correlators cannot be used as a reliable metric of chaos or lack thereof.

Published as SciPost Phys. 15, 244 (2023)

Author comments upon resubmission

Dear Editor,

We appreciate your editorial recommendation and thank the referees for their comments and willingness to publish our manuscript, provided that a suitable minor revision is made. The revised manuscript now incorporates the requested changes. We address the Referees' suggestions and queries in a detailed response to each report.

We hope that the Referees' recommendations have been appropriately addressed, enabling the publication of our work in SciPost.

Talía L.M. Lezama, Yevgeny Bar Lev, and Lea F. Santos

List of changes

1. In the Discussion section, we have explicitly stated that our analysis is applicable to quantum systems with a bounded local Hilbert space dimension and added a comment regarding the generality of our results to higher dimensions.
2. In response to Referee 1's recommendation, we have added the pertinent reference (Ref. [86]) and a corresponding comment to offer context within the Discussion section.
3. Following the optional suggestion from Referee 2, we have introduced a new sentence after Eq. (14) to provide a clearer explanation of the connection and distinctions between our results and those presented in Ref. [76].
4. We changed the format of the manuscript to single column and adapted the format of Fig. 3 accordingly.

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