Defining Time Crystals via Representation Theory

Abstract

Time crystals are proposed states of matter which spontaneously break time translation symmetry. There is no settled definition of such states. We offer a new definition which follows the traditional recipe for Wigner symmetries and order parameters. Supplementing our definition with a few plausible assumptions we find that a) systems with time independent Hamiltonians should not exhibit TTSB while b) the recently studied $\pi$ spin glass/Floquet time crystal can be viewed as breaking a global internal symmetry and as breaking time translation symmetry as befits its two names.

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Cited by in corpus (52)

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• Equilibration and Order in Quantum Floquet Matter
• Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems
• Dicke time crystals in driven-dissipative quantum many-body systems
• Classical Discrete Time Crystals
• Clean Floquet Time Crystals: Models and Realizations in Cold Atoms
• Observation of a symmetry-protected topological time crystal with superconducting qubits
• Floquet time crystals in clock models
• Emergent limit cycles and time crystal dynamics in an atom-cavity system
• Shattered Time: Can a Dissipative Time Crystal Survive Many-Body Correlations?
• Prethermalization without temperature
• Exact Floquet quantum many-body scars under Rydberg blockade
• Time crystals in a shaken atom-cavity system
• Time crystallinity in open quantum systems
• Floquet Quantum Criticality
• Condensed Matter Physics in Time Crystals
• Classical Stochastic Discrete Time Crystals
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• Dissipative time crystals with long-range Lindbladians
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• Absolutely Stable Spatiotemporal Order in Noisy Quantum Systems
• A dissipative time crystal with or without ${\mathbb{Z}}_2$ symmetry breaking
• Coherent dynamics in frustrated coupled parametric oscillators
• Realizing time crystals in discrete quantum few-body systems
• Universal presence of time-crystalline phases and period-doubling oscillations in one-dimensional Floquet topological insulators
• Strong-Disorder Renormalization Group for Periodically Driven Systems
• Stroboscopic aliasing in long-range interacting quantum systems
• Imaginary time crystal of thermal quantum matter
• Quantum frequency locking and down-conversion in a driven cavity-qubit system
• High-frequency Expansion for Floquet Prethermal Phases with Emergent Symmetries: Application to Time Crystals and Floquet Engineering
• Flow Equations for Disordered Floquet Systems
• Very slow heating for weakly driven quantum many-body systems
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• Time-crystalline behavior in an engineered spin chain
• Comment on "Quantum Time Crystals from Hamiltonians with Long-Range Interactions"
• Discrete time-crystals in unbounded potentials
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• Theory for dissipative time crystals in coupled parametric oscillators
• Swapping Floquet time crystal
• Quantum quench in a driven Ising chain
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• Multiple tunable real-space degeneracies in graphene irradiated by twisted light
• Universality in Non-Equilibrium Quantum Systems
• Controlling discrete time crystals via single-site operations in zero-field diamond quantum simulators
• Stabilizing boundary time crystals through Non-markovian dynamics
• Floquet engineering of topological phases protected by emergent symmetries under resonant drives