Spatial-Translation-Induced Discrete Time Crystals

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.