Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model

TL;DR

This paper investigates how adding a one-body interaction to the SYK model affects its quantum chaos and holographic properties, revealing a temperature-dependent transition from chaotic to integrable behavior.

Contribution

It analytically and numerically demonstrates the existence of a chaotic-integrable transition in the generalized SYK model with a one-body perturbation.

Findings

The model remains chaotic at high temperatures despite the perturbation.

A transition to integrability occurs at a specific temperature depending on the perturbation strength.

Spectral correlations change from Wigner-Dyson to Poisson statistics at the transition.

Abstract

Quantum chaos is one of the distinctive features of the Sachdev-Ye-Kitaev (SYK) model, $N$ Majorana fermions in $0+1$ dimensions with infinite-range two-body interactions, which is attracting a lot of interest as a toy model for holography. Here we show analytically and numerically that a generalized SYK model with an additional one-body infinite-range random interaction, which is a relevant perturbation in the infrared, is still quantum chaotic and retains most of its holographic features for a fixed value of the perturbation and sufficiently high temperature. However a chaotic-integrable transition, characterized by the vanishing of the Lyapunov exponent and spectral correlations given by Poisson statistics, occurs at a temperature that depends on the strength of the perturbation. We speculate about the gravity dual of this transition.