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Classical discrete time crystals
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DOI：10.1038/s41567-019-0782-3.png)
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Abstract
En 中文
The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: the discrete time crystal (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay of non-equilibrium driving, many-body interactions and the breakdown of ergodicity. However, subharmonic responses are also a well-known feature of classical dynamical systems ranging from predator-prey models to Faraday waves and a.c.-driven charge density waves. This raises the question of whether these classical phenomena display the same rigidity characteristic of a quantum DTC. In this work, we explore this question in the context of periodically driven Hamiltonian dynamics coupled to a finite-temperature bath, which provides both friction and, crucially, noise. Focusing on one-dimensional chains, where in equilibrium any transition would be forbidden at finite temperature, we provide evidence that the combination of noise and interactions drives a sharp, first-order dynamical phase transition between a discrete time-translation invariant phase and an activated classical discrete time crystal (CDTC) in which time-translation symmetry is broken out to exponentially long timescales. Power-law correlations are present along a first-order line, which terminates at a critical point. We analyse the transition by mapping it to the locked-to-sliding transition of a d.c.-driven charge density wave. Finally, building upon results from the field of probabilistic cellular automata, we conjecture the existence of classical time crystals with true long-range order, where time-translation symmetry is broken out to infinite times. The phenomenon of many-body localization gives rise to entirely new phases of quantum matter when it is driven away from equilibrium. A numerical study now shows that one of these phases-the discrete time crystal-can also occur in a classical spin chain.
Keywords:
SUBHARMONIC SHAPIRO STEPS
DYNAMICS
CHARGE
FLUCTUATIONS
ENTRAINMENT
STABILITY
FRICTION
BEHAVIOR
STATES
ORDER
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