Exact solution of a boundary time-crystal phase transition: time-translation symmetry breaking and non-Markovian dynamics of correlations
arXiv:2110.00030 · doi:10.1103/PhysRevA.105.L040202
Abstract
The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of non-stationary dynamical phases. Systems that display nonequilibrium transitions into these phases are referred to as time-crystals, and they can be realized, for example, in many-body systems governed by collective dissipation and long-ranged interactions. Here, we provide a complete analytical characterization of a boundary time-crystal phase transition. This involves exact expressions for the order parameter and for the dynamics of quantum fluctuations, which, in the time-crystalline phase, remains asymptotically non-Markovian as a consequence of the time-translation symmetry breaking. We demonstrate that boundary time-crystals are intrinsically critical phases, where fluctuations exhibit a power-law divergence with time. Our results show that a dissipative time-crystal phase is far more than merely a classical non-linear and non-stationary (limit cycle) dynamics of a macroscopic order parameter. It is rather a genuine many-body phase where the properties of correlations distinctly differs from that of stationary ones.
arXiv comment13 pages, 2 figures
References in corpus (53)
- Thermalization and its mechanism for generic isolated quantum systems
- Nonequilibrium dynamics of closed interacting quantum systems
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Decoherence Free Subspaces for Quantum Computation
- Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
- Observation of a Discrete Time Crystal
- Observation of discrete time-crystalline order in a disordered dipolar many-body system
- Floquet Time Crystals
- On the phase structure of driven quantum systems
- Quantum Time Crystals
- A Theory of Quantum Error-Correcting Codes
- Quantum spin squeezing
- Time crystals: a review
- Classical Time Crystals
- Modeling spontaneous breaking of time-translation symmetry
- Non-stationary coherent quantum many-body dynamics through dissipation
- Boundary time crystals
- Decoherence-Free Subspaces and Subsystems
- Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
- Non-Markovian quantum dynamics: local versus non-local
- Observation of a dissipative time crystal
- Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
- Floquet time crystal in the Lipkin-Meshkov-Glick model
- Observation of time quasicrystal and its transition to superfluid time crystal
- Scrambling and entanglement spreading in long-range spin chains
- Observation of a space-time crystal in a superfluid quantum gas
- Space-time crystals of trapped ions
- Temporal order in periodically driven spins in star-shaped clusters
- Dissipation Induced Structural Instability and Chiral Dynamics in a Quantum Gas
- Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems
- Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensates
- Dicke time crystals in driven-dissipative quantum many-body systems
- Classical Discrete Time Crystals
- All-Optical Dissipative Discrete Time Crystals
- Dissipation Induced Nonstationarity in a Quantum Gas
- Limit cycle phase in driven-dissipative spin systems
- Bridging entanglement dynamics and chaos in semiclassical systems
- Floquet time crystals in clock models
- The structure of preserved information in quantum processes
- Dissipation-induced instabilities of a spinor Bose-Einstein condensate inside an optical cavity
- The fate of a discrete time crystal in an open system
- Exactness of mean-field equations for open Dicke models with an application to pattern retrieval dynamics
- Origin of the slow growth of entanglement entropy in long-range interacting spin systems
- Symmetries and conserved quantities of boundary time crystals in generalized spin models
- Dynamical phases and quantum correlations in an emitter-waveguide system with feedback
- Boundary time crystals in collective -level systems
- Nonequilibrium many-body quantum engine driven by time-translation symmetry breaking
- Building continuous time crystals from rare events
- Quantum spin chain dissipative mean-field dynamics
- Non-markovian mesoscopic dissipative dynamics of open quantum spin chains
- Bistability and time crystals in long-ranged directed percolation
- Anharmonic classical time crystals: A coresonance pattern formation mechanism
- Quantum Fluctuations in Mesoscopic Systems
Cited by in corpus (43)
- Review: Quantum Metrology and Sensing with Many-Body Systems
- Dissipative time crystal in a strongly interacting Rydberg gas
- Continuous sensing and parameter estimation with the boundary time-crystal
- Quantum metrology with boundary time crystals
- Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
- Measurement Induced Continuous Time Crystals
- Quantum trajectories of dissipative time-crystals
- Mode softening in time-crystalline transitions of open quantum systems
- Signatures of discrete time-crystallinity in transport through an open Fermionic chain
- Entangled time-crystal phase in an open quantum light-matter system
- Genuine Multipartite Correlations in a Boundary Time Crystal
- Dynamical phase transitions in the nonreciprocal Ising model
- Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals
- Emergence and Dynamical Stability of Charge Time-Crystal in a Current-Carrying Quantum Dot Simulator
- Boundary Time Crystals as AC sensors: enhancements and constraints
- Quantum thermodynamics of boundary time-crystals
- Dissipative time crystals originating from parity-time symmetry
- Nonequilibrium transition between dissipative time crystals
- Nonequilibrium thermodynamics and power generation in open quantum optomechanical systems
- Exotic synchronization in continuous time crystals outside the symmetric subspace
- Non-Gaussian dynamics of quantum fluctuations and mean-field limit in open quantum central spin systems
- Quantum Fluctuation Dynamics of Dispersive Superradiant Pulses in a Hybrid Light-Matter System
- Nonstabilizerness of a Boundary Time Crystal
- Topologically protected boundary discrete time crystal for a solvable model
- Crossover from the discontinuous to continuous phase transitions in dissipative spin system with collective decay
- Symmetries & Correlations in Continous Time Crystals
- Boundary Time Crystals Induced by Local Dissipation and Long-Range Interactions
- Generation of entanglement and non-stationary states via competing coherent and incoherent bosonic hopping
- Exploiting nonequilibrium phase transitions and strong symmetries for continuous measurement of collective observables
- Opening Krylov space to access all-time dynamics via dynamical symmetries
- Dynamical phases of a BEC in a bad optical cavity at optomechanical resonance
- Time Crystals from single-molecule magnet arrays
- Thermodynamics of coupled time crystals with an application to energy storage
- Programmable time crystals from higher-order packing fields
- Nonperturbative decay of bipartite discrete time crystals
- Critical behavior of a programmable time-crystal lattice gas
- Exceptional Spectral Phase in a Dissipative Collective Spin Model
- Chaos in Time: A Dissipative Continuous Quasi Time Crystals
- Time Glasses: Symmetry Broken Chaotic Phase with a Finite Gap
- Stabilizing boundary time crystals through Non-markovian dynamics
- Lindbladian reverse engineering for general non-equilibrium steady states: A scalable null-space approach
- Dynamical Tipping in a Quantum Limit Cycle
- Parameter estimation with one- and two-time measurements on the emission field of the boundary time crystal