Dissipative time crystals with long-range Lindbladians

Abstract

Dissipative time crystals can appear in spin systems, when the $Z_2$ symmetry of the Hamiltonian is broken by the environment, and the square of total spin operator $S^2$ is conserved. In this manuscript, we relax the latter condition and show that time-translation-symmetry breaking collective oscillations persist, in the thermodynamic limit, even in the absence of spin symmetry. We engineer an \textit{ad hoc} Lindbladian using power-law decaying spin operators and show that time-translation symmetry breaking appears when the decay exponent obeys $0<\eta \le 1$. This model shows a surprisingly rich phase diagram, including the time-crystal phase as well as first-order, second-order, and continuous transitions of the fixed points. We study the phase diagram and the magnetization dynamics in the mean-field approximation. We prove that this approximation is quantitatively accurate, when $0<\eta \le 1$ and the thermodynamic limit is taken, because the system does not develop sizable quantum fluctuations, if the Gaussian approximation is considered.

arXiv comment13 pages, 11 figures

References in corpus (66)

• Decoherence Free Subspaces for Quantum Computation
• Noiseless Quantum Codes
• 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
• Discrete time crystals: rigidity, criticality, and realizations
• Time crystals: a review
• Absence of Quantum Time Crystals
• Non-stationary coherent quantum many-body dynamics through dissipation
• Boundary time crystals
• Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
• Pre-thermal phases of matter protected by time-translation symmetry
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance
• Floquet time crystal in the Lipkin-Meshkov-Glick model
• Observation of a continuous time crystal
• Scrambling and entanglement spreading in long-range spin chains
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Space-time crystals of trapped ions
• Confined Quasiparticle Dynamics in Long-Range Interacting Quantum Spin Chains
• Critical Time Crystals in Dipolar Systems
• Anomalous dynamical phase in quantum spin chains with long-range interactions
• Comment on "Quantum Time Crystals": a new paradigm or just another proposal of perpetuum mobile?
• Dicke time crystals in driven-dissipative quantum many-body systems
• Classical Discrete Time Crystals
• Clean Floquet Time Crystals: Models and Realizations in Cold Atoms
• Quantum Time Crystals from Hamiltonians with Long-Range Interactions
• Persistence of locality in systems with power-law interactions
• Prethermalization and Persistent Order in the Absence of a Thermal Phase Transition
• Relations between Short Range and Long Range Ising models
• Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model
• Higher-order and fractional discrete time crystals in clean long-range interacting systems
• Time crystals: can diamagnetic currents drive a charge density wave into rotation?
• A dissipative time crystal in an asymmetric non-linear photonic dimer
• Shattered Time: Can a Dissipative Time Crystal Survive Many-Body Correlations?
• Asymptotic Floquet states of open quantum systems: The role of interaction
• Driven Bose-Hubbard dimer under nonlocal dissipation: A bistable time crystal
• Defining Time Crystals via Representation Theory
• Symmetries and conserved quantities of boundary time crystals in generalized spin models
• Time crystal behavior of excited eigenstates
• Reverse quantum annealing of the $p$-spin model with relaxation
• Correlation engineering via non-local dissipation
• Time crystallinity in open quantum systems
• Counterdiabatic driving in the quantum annealing of the $p$-spin model: a variational approach
• Dynamical phases and quantum correlations in an emitter-waveguide system with feedback
• Boundary time crystals in collective $d$-level systems
• Spreading of correlations in exactly-solvable quantum models with long-range interactions in arbitrary dimensions
• Nonequilibrium many-body quantum engine driven by time-translation symmetry breaking
• Classical Stochastic Discrete Time Crystals
• Dynamical Phase Diagram of a Quantum Ising Chain with Long Range Interactions
• On the broken time translation symmetry in macroscopic systems: precessing states and off-diagonal long-range order
• Dynamical scaling of correlations generated by short- and long-range dissipation
• Dissipative phase transitions in the fully-connected Ising model with $p$-spin interaction
• Signatures of discrete time-crystallinity in transport through an open Fermionic chain
• Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems
• Driven-dissipative criticality within the discrete truncated Wigner approximation
• Many-body synchronisation in a classical Hamiltonian system
• Universality class of Ising critical states with long-range losses
• Driven-dissipative Ising Model: An exact field-theoretical analysis
• Bistability and time crystals in long-ranged directed percolation
• Higher order moments, cumulants, and spectra of continuous quantum noise measurements
• Entanglements and correlations of one-dimensional quantum spin-1/2 chain with anisotropic power-law long range interactions
• Standard quantum annealing outperforms adiabatic reverse annealing with decoherence

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• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals
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• Synchronization of persistent oscillations in spin systems with non-local dissipations
• Exotic synchronization in continuous time crystals outside the symmetric subspace
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• Emergent Continuous Time Crystal in Dissipative Quantum Spin System without Driving
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• Symmetries & Correlations in Continous Time Crystals
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