Scrambling under quench

TL;DR

This paper investigates out-of-time-ordered correlators in low-dimensional quantum systems after quantum quenches, revealing relationships between Lyapunov exponents, energy, and quench parameters, with specific scalings observed.

Contribution

It establishes a connection between the Lyapunov exponent and the quenched energy, linking chaos measures to quench dynamics and effective temperature.

Findings

Lyapunov exponent equals the quenched energy when it exists.

Exponent relates to the post-quench effective temperature.

Scaling of the exponent matches the energy generated during the quench.

Abstract

We evaluate out of time ordered correlators in certain low dimensional quantum systems at zero temperature, subjected to homogenous quantum quenches. We find that when the Lyapunov exponent exists, it can be identified with the quenched energy. We show that the exponent naturally gets related to the post-quench effective temperature. In the context of sudden quenches the exponent is determined in terms of the quench amplitude while for smooth quenches we observe scalings (both the Kibble-Zurek as well as the fast) of the exponent with the quench rate. The scalings are identical to that of the energy generated during the quench.