Work statistics and symmetry breaking in an excited state quantum phase transition

TL;DR

This paper investigates how excited state quantum phase transitions influence the dynamics of a many-body system, revealing non-Gaussian work distributions and entropy sensitivity near critical points, with implications for symmetry breaking effects.

Contribution

It demonstrates the manifestation of excited state quantum phase transitions in dynamics, highlighting the role of symmetry breaking and entropy as indicators, extending analysis to excited initial states.

Findings

Work probability distribution becomes non-Gaussian near critical points.

Entropy of the diagonal ensemble is highly sensitive to critical regions.

Symmetry breaking affects dynamics only beyond the critical point.

Abstract

We examine how the presence of an excited state quantum phase transition manifests in the dynamics of a many-body system subject to a sudden quench. Focusing on the Lipkin-Meshkov-Glick model initialized in the ground state of the ferromagnetic phase, we demonstrate that the work probability distribution displays non-Gaussian behavior for quenches in the vicinity of the excited state critical point. Furthermore, we show that the entropy of the diagonal ensemble is highly susceptible to critical regions, making it a robust and practical indicator of the associated spectral characteristics. We assess the role that symmetry breaking has on the ensuing dynamics, highlighting that its effect is only present for quenches beyond the critical point. Finally, we show that similar features persist when the system is initialized in an excited state and briefly explore the behavior for initial states in the paramagnetic phase.