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

### Submission summary

 As Contributors: Tomoki Nosaka Preprint link: scipost_202010_00024v1 Date submitted: 2020-10-23 17:39 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.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 2012.10628v1 on 22 December 2020

Submission scipost_202010_00024v1 on 23 October 2020

## Reports on this Submission

### Report

The author presented a nice review of his research work published earlier. The motivation and the set-up of the research were stated concisely. Given the limited space, the author presented the result of his work with the aid of plots in an effective way.

As this is a review article, one suggestion which might benefit the readers is to focus on the explanation of physics a bit more. For example, the discussion (page 4) about the phase diagram with respect to the temperature and the coupling ($\mu$) 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.

The review is interesting and well written.

### Requested changes

1- Just a small typo. On page 2, 9th line below equation (2), it should read "exhibits" instead of "exhibis".

2- Please state the definition of $\left\langle \dots \right\rangle_{ J_\alpha}$ 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.)

3-Similarly for equation 12, it is helpful to define the meaning of expectation value. (Thermal average etc.)

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