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

TL;DR

This paper investigates how a phase transition in a mass deformed SYK model affects quantum chaos, revealing a sharp change in the chaos exponent linked to a Hawking-Page-like transition.

Contribution

It demonstrates a discontinuous change in the chaos exponent at the phase transition in a coupled SYK model, connecting thermodynamic and chaotic properties.

Findings

Chaos exponent drops discontinuously at the phase transition

Hawking-Page-like transition correlates with a chaos transition

Large N bilocal field formalism used for analysis

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.