Spectral signatures of symmetry-breaking dynamical phase transitions

Abstract

Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. One of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While the Macroscopic Fluctuation Theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete ${\mathbb{Z}}_n$ symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. We show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate manifold. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in three paradigmatic many-body systems: (i) the 1D boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (ii) the $3$ and $4$-state Potts model, which displays discrete rotational symmetry-breaking DPT for energy fluctuations, and (iii) the closed WASEP which presents a continuous symmetry-breaking DPT to a time-crystal phase characterized by a rotating condensate.

30 pages, 17 figures

References in corpus (20)

• The large deviation approach to statistical mechanics
• Thermodynamic uncertainty relation for biomolecular processes
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Fluctuation theorems for stochastic dynamics
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Universal oscillations in counting statistics
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Cumulants and large deviations of the current through non-equilibrium steady states
• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state
• Symmetries in Fluctuations Far from Equilibrium
• Large fluctuations and dynamic phase transition in a system of self-propelled particles
• Multiple phases in stochastic dynamics: geometry and probabilities
• Learning nonequilibrium control forces to characterize dynamical phase transitions
• Coupled activity-current fluctuations in open quantum systems under strong symmetries
• Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
• Symmetry-induced fluctuation relations in open quantum systems

Cited by in corpus (5)

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• KPZ fluctuations in finite volume
• Programmable time crystals from higher-order packing fields
• Critical behavior of a programmable time-crystal lattice gas
• Making rare events typical in $d$-dimensional chaotic maps