Spatial-Translation-Induced Discrete Time Crystals

TL;DR

This paper introduces a novel type of discrete time crystal induced by spatial translation symmetry breaking, allowing different time crystal orders to emerge through filling changes, with potential for detection via local transport oscillations.

Contribution

It proposes the concept of spatial-translation-induced discrete time crystals (STI-DTCs), expanding the mechanisms for realizing time crystal orders beyond on-site symmetry breaking.

Findings

Local charge or spin transport exhibits nontrivial oscillations.

Time crystal orders depend on filling, not driving protocol.

New pathway for realizing time crystals via spatial translation.

Abstract

A discrete time crystal is a phase unique to nonequilibrium systems, where discrete time translation symmetry is spontaneously broken. Most of conventional time crystals proposed so far rely on spontaneous breaking of on-site symmetries and their corresponding on-site symmetry operations. In this Letter, we propose a new time crystal dubbed "spatial-translation-induced discrete time crystal (STI-DTC)", which is realized by spatial translation and its symmetry breaking. Owing to the properties of spatial translation, in this new time crystal, various time crystal orders can emerge only by changing the filling but not changing the driving protocol. We demonstrate that local transport of charges or spins shows a nontrivial oscillation, enabling detection and applications of time crystal orders. Our proposal opens up a new avenue of realizing time crystal orders by spatial translation.