Three-stage melting of a macroscopic continuous spacetime crystal

Abstract

A spacetime crystal is a phase of matter that spontaneously develops periodic order in both space and time. Spacetime crystals have been experimentally observed in microscopic quantum many-body systems and, very recently, in a mesoscopic nematic liquid crystal. However, the melting process of a spacetime crystal and its underlying physical mechanisms have not yet been experimentally reported. Here, we present a direct observation of a classical continuous spacetime crystal melting in a table-top experiment with macroscopic active granular disks in 2 + 1 spacetime dimensions. The spacetime crystal is characterized by the spontaneous formation of a coherent, rigid-body rotation of a 2D triangular lattice that persists for almost a day and remains remarkably robust to noise. By tuning the disk packing fraction, we observe a complex three-stage melting process involving a spatially hexatic phase and multiple coexistence regions. Importantly, we show that spatial and temporal crystalline orders melt separately through distinct mechanisms: Spatial order is destroyed by the proliferation of topological defects, while temporal order is lost through the decay of directional persistence caused by the progressive weakening of many-body interactions. Our results demonstrate that the spontaneous breaking of spatial and temporal translational symmetries can be decoupled, leading to the emergence of exotic out-of-equilibrium classical phases of matter.