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A sharp transition in quantum chaos and thermodynamics of mass deformed SYK model
by Tomoki Nosaka
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Submission summary
Authors (as registered SciPost users):  Tomoki Nosaka 
Submission information  

Preprint Link:  https://arxiv.org/abs/2012.10628v1 (pdf) 
Date accepted:  20210106 
Date submitted:  20201222 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 (STRHAN2020) 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We review our recent work [arXiv:2009.10759] where we studied the chaotic property of the two coupled SachdevYeKitaev systems exhibiting a HawkingPage like phase transition. By computing the outoftimeordered correlator in the large N limit by using the bilocal field formalism, we found that the chaos exponent of this model shows a discontinuous falloff at the phase transition temperature. Hence in this model the HawkingPage 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.
Author comments upon resubmission
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
Published as SciPost Phys. Proc. 4, 006 (2021)