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arXiv:1908.07530 · Physical Review X

Long-Range Prethermal Phases of Nonequilibrium Matter

Francisco Machado, Dominic V. Else, Gregory D. Kahanamoku–Meyer, Chetan Nayak, Norman Y. Yao

Published Feb 21, 2020• 106 citations
arXivHTMLPDF

Abstract

The existence of prethermal phases of matter in long-range interacting systems is remarkably robust, opening the door to the experimental realization of a novel, disorder-free, prethermal discrete time crystal in 1D.
DOI
10.1103/physrevx.10.011043

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Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Because of the notorious computational challenges of quantum many-body systems, numerical investigations in this direction have remained limited to one spatial dimension, in which long-range interactions have been proven a necessity. Here, we show that prethermal nonequilibrium phases of matter are not restricted to the quantum domain. Studying the Hamiltonian dynamics of a large three-dimensional lattice of classical spins, we provide the first numerical proof of prethermal phases of matter in a system with short-range interactions. Concretely, we find higher-order as well as fractional discrete time crystals breaking the time-translational symmetry of the drive with unexpectedly large integer as well as fractional periods. Our work paves the way toward the exploration of novel prethermal phenomena by means of classical Hamiltonian dynamics with virtually no limitations on the system's geometry or size, and thus with direct implications for experiments.
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We prove the existence of non-equilibrium phases of matter in the prethermal regime of periodically-driven, long-range interacting systems, with power-law exponent α>d\alpha > dα>d, where ddd is the dimensionality of the system. In this context, we predict the existence of a disorder-free, prethermal discrete time crystal in one dimension -- a phase strictly forbidden in the absence of long-range interactions. Finally, using a combination of analytic and numerical methods, we highlight key experimentally observable differences between such a prethermal time crystal and its many-body localized counterpart.