Universal work statistics in quenched gapless quantum systems

TL;DR

This paper investigates the universal scaling behavior of work statistics during quenches in gapless quantum systems, demonstrating power-law scaling in different regimes and analyzing a specific model with numerical validation.

Contribution

It introduces a universal framework for understanding work statistics in gapless quantum systems during quenches, connecting to the Kibble-Zurek mechanism and providing analytical and numerical insights.

Findings

Work cumulants scale with quench speed following universal power laws.

Analytical scaling matches exact numerical results for the Heisenberg XXZ chain.

Oscillatory patterns in finite systems vanish in the thermodynamic limit.

Abstract

We study the universality of work statistics performed during a quench in gapless quantum systems. We show that the cumulants of work scale separately in the fast and slow quench regimes, following a power law analogous to the universal scaling in the Kibble-Zurek mechanism for topological defect formation in phase transition. As an example, we analyze the nonequilibrium dynamics of a quenched Heisenberg XXZ chain at its critical gapless state using the bosonization picture, resulting in a Tomonaga-Luttinger liquid. The analytical scaling is in agreement with the exact numerical calculation for the fast and slow quench regimes. In finite systems, the characteristic function display an oscillatory pattern which disappears in the thermodynamic limit. This study is particularly useful for understanding the thermodynamics of adiabatic quantum computation.