Critical Quenches, OTOCs and Early-Time Chaos

TL;DR

This paper investigates the behavior of Out-of-Time-Order correlators (OTOCs) during critical quantum quenches in conformal field theories, revealing their role in distinguishing chaotic from integrable systems and exploring effects of inhomogeneity on scrambling times.

Contribution

It demonstrates how OTOCs can differentiate chaotic and integrable CFTs during critical quenches and shows how inhomogeneity can significantly extend scrambling times, with implications for non-equilibrium bounds.

Findings

OTOCs exhibit exponential Lyapunov growth in chaotic CFTs.

Inhomogeneity can induce large scrambling times even in theories with high central charge.

Universal thermal behavior emerges in low-point correlators at large times after quenches.

Abstract

In this article, we explore dynamical aspects of Out-of-Time-Order correlators (OTOCs) for critical quenches, in which an initial non-trivial state evolves with a CFT-Hamiltonian. At sufficiently large time, global critical quenches exhibit a universal thermal-behaviour in terms of low-point correlators. We demonstrate that, under such a quench, OTOCs demarcate chaotic CFTs from integrable CFTs by exhibiting a characteristic exponential Lyapunov growth for the former. Upon perturbatively introducing inhomogeneity to the global quench, we further argue and demonstrate with an example that, such a perturbation parameter can induce a parametrically large scrambling time, even for a CFT with an order one central charge. This feature may be relevant in designing measurement protocols for non-trivial OTOCs, in general. Both our global and inhomogeneous quench results bode well for an upper bound on the corresponding Lyapunov exponent, that may hold outside thermal equilibrium.