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.

Comments are very welcome! 10 pages. 7 figures

References in corpus (38)

• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Dynamical quantum phase transitions: a review
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• The resource theory of quantum reference frames: manipulations and monotones
• Observation of a dynamical topological phase transition
• How to quantify coherence: Distinguishing speakable and unspeakable notions
• Extending Noether's theorem by quantifying the asymmetry of quantum states
• Entanglement in a second order quantum phase transition
• Quantum speed limits, coherence and asymmetry
• Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
• Dynamical quantum phase transitions: scaling and universality
• Measuring the quality of a quantum reference frame: the relative entropy of frameness
• Topological classification of dynamical phase transitions
• The Thermodynamical Limit of the Lipkin-Meshkov-Glick Model
• Exploring dynamical phase transitions with cold atoms in an optical cavity
• Dynamical quantum phase transitions in systems with broken-symmetry phases
• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
• Quantum quenches, dynamical transitions and off-equilibrium quantum criticality
• Dynamical transitions and quantum quenches in mean-field models
• Mixed state dynamical quantum phase transition and emergent topology
• Dynamical Topological Quantum Phase Transitions for Mixed States
• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• Degradation of a quantum reference frame
• Exploring dynamical phase transitions and prethermalization with quantum noise of excitations
• Dynamical quantum phase transitions: a brief survey
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• The asymmetry properties of pure quantum states
• Thermodynamic length for far from equilibrium quantum systems
• Dynamical and excited-state quantum phase transitions in collective systems
• Alignment of reference frames and an operational interpretation for the G-asymmetry
• Bounding generalized relative entropies: Nonasymptotic quantum speed limits
• Constructing monotones for quantum phase references in totally dephasing channels
• Krylov Complexity and Dynamical Phase Transition in the quenched LMG model
• Work statistics and symmetry breaking in an excited state quantum phase transition
• Wehrl entropy production rate across a dynamical quantum phase transition
• Speedup of thermodynamic entropy production via quantum dynamical criticality