Quantum phases and their transitions play a pivotal role to characterize macroscopic matter. Recent studies have revealed that critical transitions reminiscent of equilibrium phase transitions can occur even out of equilibrium, as a singularity of dynamical counterpart of free energy. In this paper, we report a novel mechanism of dynamical phase transitions caused by spontaneous hidden antiunitary-symmetry breaking in periodically driven unitary dynamics. We characterize dynamical phases in such systems with nonunitary many-body operator obtained by switching space and time and find that its symmetry constrains the nature of phases and their transitions. In particular, at some parameters of stroboscopic Ising models, dynamical free energy density exhibits a critical transition with novel singularity absent in equilibrium. The criticality and its universal exponent originate from a many-body exceptional point of the nonunitary operator associated with spontaneous antiunitary-symmetry breaking. We also show that the generalized correlation function has the divergent correlation length at transition and exhibits oscillatory long-range order after symmetry breaking. Our results open up a quest for hitherto unknown phases with their hidden connection to nonunitary physics in macroscopic nonequilibrium systems, which can be tested in state-of-the-art quantum simulators.
Quantum phases and their transitions play a pivotal role to characterize macroscopic matter. Recent studies have revealed that critical transitions reminiscent of equilibrium phase transitions can occur even out of equilibrium, as a singularity of dynamical counterpart of free energy. In this paper, we report a novel mechanism of dynamical phase transitions caused by spontaneous hidden antiunitary-symmetry breaking in periodically driven unitary dynamics. We characterize dynamical phases in such systems with nonunitary many-body operator obtained by switching space and time and find that its symmetry constrains the nature of phases and their transitions. In particular, at some parameters of stroboscopic Ising models, dynamical free energy density exhibits a critical transition with novel singularity absent in equilibrium. The criticality and its universal exponent originate from a many-body exceptional point of the nonunitary operator associated with spontaneous antiunitary-symmetry breaking. We also show that the generalized correlation function has the divergent correlation length at transition and exhibits oscillatory long-range order after symmetry breaking. Our results open up a quest for hitherto unknown phases with their hidden connection to nonunitary physics in macroscopic nonequilibrium systems, which can be tested in state-of-the-art quantum simulators.
Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a dynamical version of free energy, their nature is yet to be elusive. Here, we show that spontaneous symmetry breaking can occur at a short-time regime and causes universal dynamical quantum phase transitions in periodically driven unitary dynamics. Unlike conventional phase transitions, the relevant symmetry is antiunitary: its breaking is accompanied by a many-body exceptional point of a nonunitary operator obtained by space-time duality. Using a stroboscopic Ising model, we demonstrate the existence of distinct phases and unconventional singularity of dynamical free energy, whose signature can be accessed through quasilocal operators. Our results open up research for hitherto unknown phases in short-time regimes, where time serves as another pivotal parameter, with their hidden connection to nonunitary physics.
Uncovering and understanding universal dynamics in matter far from equilibrium remains a key challenge. In this work, we identify a so far unrecognized form of universal behavior that emerges after a sudden symmetry-breaking quench at continuous phase transitions. Our key observation is that the order-parameter fluctuations in Ising models exhibit a compelling temporal collapse across a wide range of system sizes and quench strengths, indicative of an emergent single-variable scaling form. This phenomenon can be explained by introducing a so far unknown dynamical critical exponent for the underlying continuous phase transition. We find evidence for a lower critical effective dimension of this universal regime: it is observed in the 2D quantum and 3D and 4D classical Ising models, but not in the 1D quantum or 2D classical cases. Our results suggest that our observed universal far-from-equilibrium scaling may extend beyond the Ising models studied here and could more broadly characterize systems with non-conserved order parameters, opening new avenues for exploring universal dynamics both theoretically and in current experimental platforms.
Abstract Extending notions of phase transitions to nonequilibrium realm is a fundamental problem for statistical mechanics. While it was discovered that critical transitions occur even for transient states before relaxation as the singularity of a dynamical version of free energy, their nature is yet to be elusive. Here, we show that spontaneous symmetry breaking can occur at a short-time regime and causes universal dynamical quantum phase transitions in periodically driven unitary dynamics. Unlike conventional phase transitions, the relevant symmetry is antiunitary: its breaking is accompanied by a many-body exceptional point of a nonunitary operator obtained by space-time duality. Using a stroboscopic Ising model, we demonstrate the existence of distinct phases and unconventional singularity of dynamical free energy, whose signature can be accessed through quasilocal operators. Our results open up research for hitherto unknown phases in short-time regimes, where time serves as another pivotal parameter, with their hidden connection to nonunitary physics.
Periodically driven quantum systems can host nonequilibrium phenomena without static analogs, including in their entanglement dynamics. Here, we discover temporal entanglement transitions (TETs) in a Floquet spin chain, which correspond to a quantum phase transition in the spectrum of the entanglement Hamiltonian and are signaled by dynamical spontaneous symmetry breaking. We identify the symmetry principles underlying these transitions: they appear when the driven Hamiltonian preserves global symmetry (here, Z_{2}), the initial state respects this symmetry, and the reduced density matrix carries weight in both subsystem-parity sectors, with TETs occurring precisely when the sector weights become equal (given the previous two conditions are also satisfied). Intriguingly, we find these transitions across a broad range of driving frequencies (from adiabatic to high-frequency regime) and independent of drive details, where they manifest as periodic, sharp entanglement spectrum reorganizations marked by the Schmidt-gap closure, a vanishing entanglement echo, and symmetry-quantum-number flips, while remaining invisible to conventional local observables. At high frequencies, the entanglement Hamiltonian acquires an intrinsic timescale decoupled from the drive period, rendering the transitions genuine steady-state features. Finite-size scaling reveals universal critical behavior with correlation-length exponent ν=1, matching equilibrium Ising universality despite its emergence from purely dynamical mechanisms decoupled from static criticality. Our Letter establishes TETs as novel features in Floquet quantum matter.
Continuous time-translation symmetry is often spontaneously broken in open quantum systems, and the condition for their emergence has been actively investigated. However, there are only a few cases in which its condition for appearance has been fully elucidated. In this Letter, we show that a Lindbladian parity-time (PT) symmetry can generically produce persistent periodic oscillations in a wide class of systems. This includes one-collective spin models, which have been studied thoroughly in the context of dissipative continuous time crystals, and spatially extended bipartite bosonic systems with a conserved particle number. By making an analogy to nonreciprocal phase transitions, we demonstrate that a transition point from the dynamical phase is associated with spontaneous PT symmetry breaking that typically corresponds to a critical exceptional point. Interestingly, the periodic orbits in the PT symmetric phase are found to be center type, implying an initial state dependence. These results are established by proving that the Lindbladian PT symmetry at the microscopic level implies a nonlinear PT symmetry and by performing a linear stability analysis near the transition point. This research will further our understanding of novel nonequilibrium phases of matter and phase transitions with spontaneous antiunitary symmetry breaking.
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. Some 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 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 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. In particular, we show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate subspace. 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 several paradigmatic many-body systems, including (1) the one-dimensional boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (2) the three- and four-state Potts model for spin dynamics, which displays discrete rotational symmetry-breaking DPTs for energy fluctuations, and (3) the closed WASEP which presents a continuous symmetry-breaking DPT into a time-crystal phase characterized by a rotating condensate.