Scaling properties of work fluctuations after quenches at quantum transitions

TL;DR

This paper investigates how the distribution of work done during quantum quenches near phase transitions scales with system size, using a finite-size scaling approach validated in quantum Ising and Bose-Hubbard models.

Contribution

It introduces a dynamic finite-size scaling framework for work statistics at quantum phase transitions, applicable to various transition types and validated through analytical and numerical methods.

Findings

Established a nontrivial finite-size scaling limit for work distribution.

Verified scaling behaviors in quantum Ising and Bose-Hubbard models.

Demonstrated the universality of the scaling properties across different models.

Abstract

We study the scaling properties of the statistics of the work done on a generic many-body system at a quantum phase transition of any order and type, arising from quenches of a driving control parameter. For this purpose we exploit a dynamic finite-size scaling framework. Namely, we put forward the existence of a nontrivial finite-size scaling limit for the work distribution, defined as the large-size limit when appropriate scaling variables are kept fixed. The corresponding scaling behaviors are thoroughly verified by means of analytical and numerical calculations in two paradigmatic many-body systems as the quantum Ising model and the Bose-Hubbard model.