Onset of Quantum Chaos in Random Field Theories

TL;DR

This paper investigates the onset of quantum chaos in disordered theories, deriving self-consistent equations for correlation functions and exploring how quantum Lyapunov exponents evolve with coupling strength, revealing a transition similar to classical chaos.

Contribution

It generalizes SYK-like models to include disorder couplings as marginal deformations, enabling analysis of chaos transition from weak to strong coupling.

Findings

Discontinuous transition into chaos observed.

Derived self-consistency equations for large N models.

Quantum Lyapunov exponent behavior mimics classical KAM transition.

Abstract

We study the quantum Lyapunov exponent $\lambda_L$ 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 $\lambda_L$ from weak to strong coupling. We find interesting behaviors, including a discontinuous transition into chaos, mimicking classical KAM theory.