Exact work statistics of quantum quenches in the anisotropic XY model

TL;DR

This paper provides exact formulas for work and fluctuations during quantum quenches in the anisotropic XY model, revealing critical behavior and irreversible entropy production near quantum phase transitions.

Contribution

It derives exact analytic expressions for work statistics in quantum quenches of the XY model, highlighting non-analytic behavior at critical points.

Findings

Work fluctuations exhibit non-analytic behavior at quantum critical points.

Irreversible entropy production increases as the excitation gap closes.

Exact formulas enable analysis of work and fluctuations in ground state quenches.

Abstract

We derive exact analytic expressions for the average work done and work fluctuations in instantaneous quenches of the ground and thermal states of a one-dimensional anisotropic XY model. The average work and a quantum fluctuation relation is used to determine the amount of irreversible entropy produced during the quench, eventually revealing how the closing of the excitation gap leads to increased dissipated work. The work fluctuation is calculated and shown to exhibit non-analytic behavior as the pre-quench anisotropy parameter and transverse field are tuned across quantum critical points. Exact compact formulas for the average work and work fluctuation in ground state quenches of the transverse field Ising model allow us to calculate the first singular derivative at the critical field values.