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A sharp transition in quantum chaos and thermodynamics of mass deformed SYK model

by Tomoki Nosaka

Submission summary

As Contributors: Tomoki Nosaka
Arxiv Link: https://arxiv.org/abs/2012.10628v1 (pdf)
Date accepted: 2021-01-06
Date submitted: 2020-12-22 06:14
Submitted by: Nosaka, Tomoki
Submitted to: SciPost Physics Proceedings
Proceedings issue: 4th International Conference on Holography, String Theory and Discrete Approach in Hanoi
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
Approach: Theoretical

Abstract

We review our recent work [arXiv:2009.10759] where we studied the chaotic property of the two coupled Sachdev-Ye-Kitaev systems exhibiting a Hawking-Page like phase transition. By computing the out-of-time-ordered correlator in the large N limit by using the bilocal field formalism, we found that the chaos exponent of this model shows a discontinuous fall-off at the phase transition temperature. Hence in this model the Hawking-Page like transition is correlated with a transition in chaoticity, as expected from the relation between a black hole geometry and the chaotic behavior in the dual field theory.

Published as SciPost Phys. Proc. 4, 006 (2021)



Author comments upon resubmission

I appreciate the referee's careful reading and useful suggestions. Taking into account the referee's suggestions I revised the manuscript as described in List of changes.

List of changes

Following the requested change:
> 1- Please state the definition of ⟨…⟩Jα in equation 7. (I presume it refers to disorder average discussed in the first paragraph of section 2 but a clear definition would be helpful.)

I split eq(7) into eq(7) and eq(8), where eq(8) in the new version describes the definition of <...>_{J_\alpha} as the disorder average.

Following the requested change:
> 2- Similarly for equation 12, it is helpful to define the meaning of expectation value. (Thermal average etc.)

I modified the sentence below eq(12) (eq(13) in the new version) to clarify the definition of the average <...> as the disorder average of the thermal expectation value.

Following the requested change:
> 3- The discussion (page 4) about the phase diagram with respect to the temperature and the coupling (μ) is very interesting but somewhat limited. A slightly more elaborated discussion or explanation about the physics or implication behind the result would definitely be welcome.

I added in the paragraph below eq(11) (eq(12) in the new version) some detailed descriptions of the two phases. Along with this modification, I also replaced Figure 1(left) by adding the result for the two uncoupled SYK models to show that the free energy in the high temperature phase approaches this result.

Following the requested change:
> 4- A small typo. On page 2, 9th line below equation (2), it should read "exhibits" instead of "exhibis".

I fixed the typo. I also fixed the following typos

- 8th line in pp.3: transiion -> transition
- 20th line in pp.3: trnasition -> transition
- 1st line of section 4 in pp.6: reviwed -> reviewed

Submission & Refereeing History

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Resubmission 2012.10628v1 on 22 December 2020

Reports on this Submission

Anonymous Report 1 on 2020-12-25 (Invited Report)

Report

The author has responded to the previous suggestions and edited the article accordingly. The article is ready for publication.

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