More on chaos at weak coupling

TL;DR

This paper investigates the quantum Lyapunov exponent in SYK-like models with marginal interactions, proving a conjecture in 1D and providing evidence for a 2D generalization, enhancing understanding of chaos at weak coupling.

Contribution

It proves a conjecture relating Lyapunov exponents to decoupled theories in 1D and offers new examples and evidence for similar behavior in 2D models at weak coupling.

Findings

In 1D, Lyapunov exponent at small coupling matches a specific limit of the four-point function.

Provides new examples of Lyapunov exponents in 2D models at weak coupling.

Supports the conjecture that chaos measures can be derived from decoupled theories in low dimensions.

Abstract

We discuss aspects of the quantum Lyapunov exponent $\lambda_L$ in theories with an exactly marginal SYK-like random interaction, where $\lambda_L$ can be computed as a continuous function of the interaction strength $\mathcal{J}$. In $1d$, we prove a conjecture from arXiv:2111.06108 which states that at small $\mathcal{J}$, $\lambda_L$ can be found by considering a specific limit of the four-point function in the decoupled theory. We then provide additional evidence for the $2d$ version of this conjecture by discussing new examples of Lyapunov exponents which can be computed at weak coupling.