SYK Model, Chaos and Conserved Charge

TL;DR

This paper analyzes the complex fermion SYK model with a chemical potential, revealing how the Lyapunov exponent, indicative of chaos, varies with chemical potential and can be suppressed even at large coupling.

Contribution

It provides an exact solution for the large q limit of the complex fermion SYK model with chemical potential and semi-analytical calculation of the Lyapunov exponent.

Findings

Lyapunov exponent depends sensitively on chemical potential

Small chemical potentials can suppress chaos even at large coupling

Exact solutions in the large q limit

Abstract

We study the SYK model with complex fermions, in the presence of an all-to-all $q$-body interaction, with a non-vanishing chemical potential. We find that, in the large $q$ limit, this model can be solved exactly and the corresponding Lyapunov exponent can be obtained semi-analytically. The resulting Lyapunov exponent is a sensitive function of the chemical potential $\mu$. Even when the coupling $J$, which corresponds to the disorder averaged values of the all to all fermion interaction, is large, values of $\mu$ which are exponentially small compared to $J$ lead to suppression of the Lyapunov exponent.