Chaos in a classical limit of the Sachdev-Ye-Kitaev model

TL;DR

This paper investigates chaos in a classical limit of the SYK model, revealing a temperature-dependent Lyapunov exponent and mapping the dynamics to a rotating N-dimensional body with a spin glass phase.

Contribution

It introduces a classical limit of the SYK model, analyzes chaos and thermodynamics, and connects the dynamics to a rotating body with fixed points and a p-spin spin glass phase.

Findings

Lyapunov exponent depends linearly on temperature with a different slope than quantum case

Classical dynamics modeled as rotation of an N-dimensional body with random inertia

Presence of spin glass phase at low temperature does not prevent chaos

Abstract

We study chaos in a classical limit of the Sachdev-Ye-Kitaev (SYK) model obtained in a suitably defined large-S limit. The low-temperature Lyapunov exponent is found to depend linearly on temperature, with a slope that is parametrically different than in the quantum case: it is proportional to N/S. The classical dynamics can be understood as the rotation of an N-dimensional body with a random inertia tensor, corresponding to the random couplings of the SYK Hamiltonian. This allows us to find an extensive number of fixed points, corresponding to the body's principal axes of rotation. The thermodynamics is mapped to the p-spin model with p=2, which exhibits a spin glass phase at low temperature whose presence does not preclude the existence of chaos.