# Homogeneous Floquet time crystal protected by gauge invariance

## TL;DR

This paper demonstrates that homogeneous lattice gauge theories can host long-range nonequilibrium phases like time crystals, protected by gauge invariance rather than disorder, with robustness confirmed through analytical and numerical methods.

## Contribution

It introduces a novel mechanism for realizing and protecting time crystals in gauge theories, expanding the understanding of nonequilibrium phases beyond disordered systems.

## Key findings

- Homogeneous gauge theories can exhibit time-crystal behavior.
- The time crystal phase is robust against certain perturbations.
- Analytical and numerical evidence supports long-range spatiotemporal order.

## Abstract

We show that homogeneous lattice gauge theories can realize nonequilibrium quantum phases with long-range spatiotemporal order protected by gauge invariance instead of disorder. We study a kicked $\mathbb{Z}_2$-Higgs gauge theory and find that it breaks the discrete temporal symmetry by a period doubling. In a limit solvable by Jordan-Wigner analysis we extensively study the time-crystal properties for large systems and further find that the spatiotemporal order is robust under the addition of a solvability-breaking perturbation preserving the $\mathbb{Z}_2$ gauge symmetry. The protecting mechanism for the nonequilibrium order relies on the Hilbert space structure of lattice gauge theories, so that our results can be directly extended to other models with discrete gauge symmetries.