Onset of Quantum Chaos in Random Field Theories

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