Asymmetry and dynamical criticality

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.

The paper asks whether quantum-asymmetry measures diagnose dynamical quantum phase transitions (DQPTs) and connect their symmetry structure to nonequilibrium thermodynamics. It studies sudden transverse-field quenches in the Lipkin–Meshkov–Glick model, $H=-(J/j)(J_z^2+\gamma J_y^2)-2hJ_x$, using the trace-norm commutator $F_L(\rho)=\|[\rho,L]\|_1$ for $L=J_x,J_y,J_z$. Parity is a discrete rotation about $x$; the measures instead quantify asymmetry under continuous rotations. The main evidence is numerical time evolution and time averaging, principally at $J=1$, $j=100$ ($N=200$), starting from the ground state at $h_0=0$. Comparisons include quenches to $h=0.2$ and $0.8$, anisotropies $\gamma=0.2$ and $0.8$, and scans over $(h,\gamma)$. Time-averaged asymmetry develops peaks or rapid changes near the dynamical transition: around $h\approx0.5$ for $\gamma=0.2$ and $h\approx0.4$ for $\gamma=0.8$. These features track the decay of time-averaged $z$ magnetization and features in a Bures-angle lower bound on entropy production. The $J_z$ measure gives the sharpest numerical signature, while $J_x$ is interpreted in relation to parity restoration. The signatures weaken toward the isotropic limit $\gamma=1$, where the specified quench produces trivial evolution. The analysis is restricted to sudden quenches in this collective-spin model and establishes correspondence between diagnostics rather than a general quantitative relation. The paper explicitly limits applicability to systems where symmetry-related mechanisms underlie critical dynamics; other asymmetry measures, finite-time ramps, finite-temperature states, open systems, and broader model classes remain proposed extensions.