Phase transition and chaos in charged SYK model

TL;DR

This paper investigates the transition between chaos and integrability in the charged SYK model with chemical potential, revealing a phase transition and the suppression of chaos as chemical potential increases.

Contribution

It introduces a novel numerical method to compute the partition function and demonstrates the impact of chemical potential on chaos and phase transition in the SYK model.

Findings

Phase transition occurs at large chemical potential.

Chemical potential suppresses Lyapunov exponent exponentially.

Mass-like term does not induce a sharp transition.

Abstract

We study chaotic-integrable transition and the nature of quantum chaos in SYK model with chemical potential. We use a novel numerical technique to calculate the partition function explicitly. We show the phase transition in the presence of large chemical potential. We also show that a mass-like term consisting of two fermion random interaction (q=2 SYK term) does not give rise to a sharp transition. We find that turning on the chemical potential suppresses the Lyapunov exponent in the chaotic phase exponentially.