The onset of quantum chaos in disordered CFTs

TL;DR

This paper investigates how quantum chaos, measured by the Lyapunov exponent, evolves in disordered conformal field theories as the disorder strength varies, revealing unexpected transitions and providing a framework for analysis.

Contribution

It introduces exactly marginal disorder deformations in CFTs, enabling continuous tracking of chaos from weak to strong coupling, and derives self-consistency equations for correlators in disordered CFT products.

Findings

Discontinuous transition into chaos observed in some models

Lyapunov exponent can be tracked across coupling regimes

Derived equations for correlators in disordered CFTs

Abstract

We study the Lyapunov exponent $\lambda_L$ in quantum field theories with spacetime-independent disorder interactions. Generically $\lambda_L$ can only be computed at isolated points in parameter space, and little is known about the way in which chaos grows as we deform the theory away from weak coupling. In this paper we describe 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 surprising behaviors in some cases, including a discontinuous transition into chaos. We also derive self-consistency equations for the two- and four-point functions for products of $N$ nontrivial CFTs deformed by disorder at leading order in $1/N$.