Work fluctuations in quantum spin chains

TL;DR

This paper investigates work fluctuations in finite quantum spin chains under time-dependent magnetic fields, testing fluctuation relations and revealing distinct behaviors in integrable and nonintegrable models.

Contribution

It provides a numerical validation of fluctuation relations in quantum spin chains and offers an exact solution for the Ising case with insights into work fluctuation behaviors.

Findings

Fluctuation relations are numerically validated for both models.

Work fluctuations peak at a frequency proportional to the magnetic field amplitude.

A sharp transition in work distribution is observed in the nonintegrable chain depending on field frequency.

Abstract

We study the work fluctuations of two types of finite quantum spin chains under the application of a time-dependent magnetic field in the context of the fluctuation relation and Jarzynski equality. The two types of quantum chains correspond to the integrable Ising quantum chain and the nonintegrable XX quantum chain in a longitudinal magnetic field. For several magnetic field protocols, the quantum Crooks and Jarzynski relations are numerically tested and fulfilled. As a more interesting situation, we consider the forcing regime where a periodic magnetic field is applied. In the Ising case we give an exact solution in terms of double-confluent Heun functions. We show that the fluctuations of the work performed by the external periodic drift are maximum at a frequency proportional to the amplitude of the field. In the nonintegrable case, we show that depending on the field frequency a sharp transition is observed between a Poisson-limit work distribution at high frequencies toward a normal work distribution at low frequencies.