Boundary Time Crystals Induced by Local Dissipation and Long-Range Interactions

Driven-dissipative many-body system supports nontrivial quantum phases absent in equilibrium. As a prominent example, the interplay between coherent driving and collective dissipation can lead to a dynamical quantum phase that spontaneously breaks time-translation symmetry. This so-called boundary time crystal (BTC) is fragile in the presence of local dissipation, which can easily relax the system to a stationary state. In this work, we demonstrate a robust BTC that is intrinsically induced by local dissipation. We provide extensive numerical evidences to support existence of the BTC and study its behaviors in different regimes. In particular, with decreasing interaction range, we identify a transition from classical limit cycles to quantum BTCs featuring sizable spatial correlations. Our studies significantly broaden the scope of nonequilibrium phases and shed new light on experimental search for dynamical quantum matter.