Synchronization of persistent oscillations in spin systems with nonlocal dissipation

We explore the synchronization phenomenon in quantum few-body system of spins with nonlocal dissipation. Without external driving, we find that can exhibit stable oscillatory behaviors long-time dynamics accompanied by appearance purely imaginary eigenvalues Liouvillian. Moreover, oscillations next-nearest-neighboring are completely synchronized, which is revealed trajectory analysis within stochastic Schr\"odinger equation. The possibility an infinite-size lattice means cluster mean-field approximation also discussed.