Classical approaches to prethermal discrete time crystals in one, two, and three dimensions

TL;DR

This paper explores how classical Hamiltonian dynamics can produce prethermal discrete time crystals across different dimensions and interaction ranges, revealing the conditions for their stability in non-equilibrium phases.

Contribution

It provides a comprehensive classical analysis of prethermal discrete time crystals in 1D, 2D, and 3D lattices with power-law interactions, extending previous quantum-focused work.

Findings

Prethermal time crystals can be stabilized in classical systems.

Dimensionality and interaction range critically affect phase stability.

Classical models complement quantum approaches to non-equilibrium phases.

Abstract

We provide a comprehensive account of prethermal discrete time crystals within classical Hamiltonian dynamics, complementing and extending our recent work [Phys. Rev. Lett. 127, 140602 (2021)]. Considering power-law interacting spins on one-, two-, and three-dimensional hypercubic lattices, we investigate the interplay between dimensionality and interaction range in the stabilization of these non-equilibrium phases of matter that break the discrete time-translational symmetry of a periodic drive.