Classical Prethermal Phases of Matter

TL;DR

This paper demonstrates that prethermal phases of matter, including time crystals, can exist in classical three-dimensional spin systems with short-range interactions, expanding the understanding beyond quantum systems.

Contribution

It provides the first numerical evidence of prethermal phases in classical Hamiltonian systems with short-range interactions in three dimensions.

Findings

Discovery of higher-order and fractional discrete time crystals.

Prethermal phases observed in classical 3D spin systems.

Implications for experimental exploration of prethermal phenomena.

Abstract

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. Due to 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 non-equilibrium 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 towards 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.