Onset of Quantum Chaos in Random Field Theories

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.

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

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• The onset of quantum chaos in disordered CFTs
• Disordered $\mathcal{N}=(2,2)$ Supersymmetric Field Theories