Onset of Quantum Chaos in Random Field Theories

Abstract

We study the quantum Lyapunov exponent $\hat{I}{»}_L$ in theories with spacetime-independent disorder. We first derive self-consistency equations for the two- and four-point functions for products of $N$ models coupled by disorder at large $N$, generalizing the equations appearing in SYK-like models. We then study families of theories in which the disorder coupling is an exactly marginal deformation, allowing us to follow $\hat{I}{»}_L$ from weak to strong coupling. We find interesting behaviors, including a discontinuous transition into chaos, mimicking classical KAM theory.

This is a summary of the more detailed article arXiv:2111.06108, to be published in PRL