Asymmetry and dynamical criticality

TL;DR

This paper links symmetry properties and quantum asymmetry measures to dynamical quantum criticality, demonstrating their effectiveness in detecting phase transitions in a many-body quantum model.

Contribution

It introduces asymmetry monotones as robust indicators of dynamical quantum phase transitions, connecting symmetry, information theory, and thermodynamics.

Findings

Asymmetry measures detect the onset of DQPTs in the Lipkin-Meshkov-Glick model.

Time-averaged asymmetry signals the dynamical critical point and correlates with entropy production.

Peaks in asymmetry coincide with maximal entropy production across the transition.

Abstract

Symmetries play a central role in both equilibrium and nonequilibrium phase transitions, yet their quantitative characterization in dynamical quantum phase transitions (DQPTs) remains an open challenge. In this work, we establish a direct connection between symmetry properties of a many-body model and measures of quantum asymmetry, showing that asymmetry monotones provide a robust and physically transparent indicator of dynamical quantum criticality. Focusing on the quenched Lipkin-Meshkov-Glick model, we demonstrate that asymmetry measures associated with collective spin generators faithfully capture the onset of DQPTs, reflecting the dynamical restoration or breaking of underlying symmetries. Remarkably, the time-averaged asymmetry exhibits clear signatures of the dynamical critical point, in close correspondence with both the dynamical order parameter and the behavior of entropy production. We further uncover a quantitative link between asymmetry generation and thermodynamic irreversibility, showing that peaks in asymmetry coincide with maximal entropy production across the transition. Our results position asymmetry as a unifying concept bridging symmetry, information-theoretic quantifiers, and nonequilibrium thermodynamics in dynamical quantum phase transitions, providing a powerful framework for understanding critical dynamics beyond traditional order parameters.