Discrete spacetime crystal: Intertwined spacetime symmetry breaking in a driven-dissipative spin system

TL;DR

This paper introduces a novel non-equilibrium phase called the 'discrete spacetime crystal' in a driven-dissipative spin system, exhibiting intertwined space-time symmetry breaking with long-range order and robustness against noise.

Contribution

It demonstrates the existence of a new nonmagnetic phase with intertwined space-time order and analyzes its stability and potential experimental realizations.

Findings

Discovery of a discrete spacetime crystal phase

Long-lived space-time order resistant to noise

Potential experimental platforms discussed

Abstract

Non-equilibrium driving systems provide fertile ground for exploring intriguing spontaneous symmetry breaking phenomena. In this study, we report on the intertwined discrete spacetime translational symmetry breaking in a driven-dissipative spin system without pure spatial translational symmetry, resulting in the emergence of an out-of-equilibrium nonmagnetic phase termed the "discrete spacetime crystal." In contrast to the previously widely studied discrete time crystal, the spins establish a distinctive long-range crystalline order not only in time, but also in the intertwined spacetime direction. We further demonstrate the exponentially-long lifetime of the spatial-temporal order against generic weak environmental noise fluctuations. Finally, possible experimental realizations of our model are discussed. Our findings shed light on the existence of exotic phases of matter characterized by intertwined space-time symmetry breaking, paving the way for future investigations into the properties and potential applications of these exotic states.