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

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