Discrete time crystals: rigidity, criticality, and realizations

Abstract

Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.

9 pages, 7 figures; V3: Modified Eqn. (1) to include coupling strength disorder which was included in the numerics and also essential for stabilizing time crystalline order. Other typos corrected and a few references added

References in corpus (7)

• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Absence of Quantum Time Crystals
• Periodically driven ergodic and many-body localized quantum systems
• Absolute Stability and Spatiotemporal Long-Range Order in Floquet systems
• Strongly interacting bosons in a disordered optical lattice
• Quantum criticality of hot random spin chains

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