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arXiv:1607.05277 · Physical Review X

Prethermal Phases of Matter Protected by Time-Translation Symmetry

Dominic V. Else, Bela Bauer, Chetan Nayak

Published Mar 7, 2017• 354 citations
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Abstract

In systems driven by time-varying fields, new phases of matter might exist that do not appear when the system is static. A mathematical formulation shows that novel phases of matter also exist in prethermal states, where the system exchanges heat with its environment very slowly.
DOI
10.1103/physrevx.7.011026

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•Aug 20, 2019•1 citation
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.
Prethermalization refers to the physical phenomenon where a system evolves toward some long-lived non-equilibrium steady state before eventual thermalization sets in. One general scenario where this occurs is in driven systems with dynamics governed by an effective Hamiltonian (in some rotating frame), such that ergodicity of the latter is responsible for the approach to the prethermal state. This begs the question whether it is possible to have a prethermal state not associated to any effective Hamiltonian. Here, we answer this question in the affirmative. We exhibit a natural class of systems in which the prethermal state is defined by emergent, global symmetries, but where the dynamics that takes the system to this state has no additional conservation laws, in particular energy. We explain how novel prethermal phases of matter can nevertheless emerge under such settings, distinct from those previously discussed.
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.