Synchronization of persistent oscillations in spin systems with nonlocal dissipation

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