Lyapunov exponents in a Sachdev-Ye-Kitaev-type model with population imbalance in the conformal limit and beyond

TL;DR

This study numerically analyzes a SYK-type model with two fermion populations, revealing that the Lyapunov exponent remains maximal and constant across different coupling regimes and population ratios, extending understanding of chaos in such models.

Contribution

It introduces a SYK-type model with population imbalance and demonstrates the Lyapunov exponent's invariance beyond the conformal limit, providing new insights into chaos in these systems.

Findings

Lyapunov exponent remains maximal at strong coupling.

Lyapunov exponent is constant across population ratios.

The invariance extends beyond the conformal limit.

Abstract

The Sachdev-Ye-Kitaev (SYK) model shows chaotic behavior with a maximal Lyapunov exponent. In this paper, we investigate the four-point function of a SYK-type model numerically, which gives us access to its Lyapunov exponent. The model consists of two sets of Majorana fermions, called A and B, and the interactions are restricted to being exclusively pairwise between the two sets, not within the sets. We find that the Lyapunov exponent is still maximal at strong coupling. Furthermore, we show that even though the conformal dimensions of the A and B fermions change with the population ratio, the Lyapunov exponent remains constant, not just in the conformal limit where it is maximal, but also in the intermediate and weak coupling regimes.