Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model

Recent discoveries have highlighted the significance of replica wormholes in resolving the information paradox and establishing the unitarity of black hole evaporation. In this letter, we propose the dissipative Sachdev-Ye-Kitaev model (SYK) as a minimal quantum model that exhibits entanglement dynamics with features qualitatively similar to replica wormholes. As a demonstration, we investigate the entanglement growth of a pair of dissipative SYK models initialized in a thermofield double state (TFD). In the regime of large $N$ with weak dissipation, we observe a first-order entanglement transition characterized by a switch of the dominant saddle point: from replica diagonal solutions for short times to replica wormhole-like off-diagonal solutions for long times. Furthermore, we show that signature of replica wormholes persists even at moderate $N\lesssim 30$ by using the Monte Carlo quantum trajectory method. Our work paves the way for explorations of replica wormhole physics in quantum simulators.