Out-of-Time-Order correlators in driven conformal field theories

TL;DR

This paper analyzes how out-of-time-order correlators behave in driven conformal field theories, revealing different dynamical phases and distinguishing integrable from chaotic models through their growth patterns.

Contribution

It provides explicit calculations of OTOCs in driven CFTs, identifying characteristic behaviors in heating and non-heating phases, and introduces a method to differentiate integrable and chaotic models under periodic drive.

Findings

OTOCs show exponential, oscillatory, and power-law behaviors in different phases.

In integrable Ising CFT, OTOCs do not exhibit exponential growth.

Drive parameters influence butterfly velocity and Lyapunov exponent.

Abstract

We compute Out-of-Time-Order correlators (OTOCs) for conformal field theories (CFTs) subjected to either continuous or discrete periodic drive protocols. This is achieved by an appropriate analytic continuation of the stroboscopic time. After detailing the general structure, we perform explicit calculations in large-$c$ CFTs where we find that OTOCs display an exponential, an oscillatory and a power-law behaviour in the heating phase, the non-heating phase and on the phase boundary, respectively. In contrast to this, for the Ising CFT representing an integrable model, OTOCs never display such exponential growth. This observation hints towards how OTOCs can demarcate between integrable and chaotic CFT models subjected to a periodic drive. We further explore properties of the light-cone which is characterized by the corresponding butterfly velocity as well as the Lyapunov exponent. Interestingly, as a consequence of the spatial inhomogeneity introduced by the drive, the butterfly velocity, in these systems, has an explicit dependence on the initial location of the operators. We chart out the dependence of the Lyapunov exponent and the butterfly velocities on the frequency and amplitude of the drive for both protocols and discuss the fixed point structure which differentiates such driven CFTs from their un-driven counterparts.