Asymmetry and dynamical criticality

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.

💡 Research Summary

In this work the authors address a long‑standing challenge in the study of dynamical quantum phase transitions (DQPTs): how to quantify the breaking and restoration of symmetries during nonequilibrium evolution in a way that goes beyond traditional order parameters and Loschmidt‑echo rate functions. They propose to use quantum asymmetry monotones—information‑theoretic quantities that measure how much a quantum state fails to commute with a chosen symmetry generator—as a universal diagnostic tool. Specifically, they adopt the ℓ₁‑norm based asymmetry measure
(F_{L}(\rho)=|