Entanglement transition and replica wormholes in the dissipative Sachdev-Ye-Kitaev model
Hanteng Wang, Chang Liu, Pengfei Zhang, Antonio M. Garcı́a-Garcı́a
Abstract
Recent discoveries have highlighted the significance of replica wormholes in resolving the information paradox and establishing the unitarity of black hole evaporation. In this paper, we propose the dissipative Sachdev-Ye-Kitaev (SYK) model 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. 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 wormholelike off-diagonal solutions for long times. Furthermore, we show that the signature of replica wormholes persists even at moderate $N\ensuremath{\lesssim}30$ by using the Monte Carlo quantum trajectory method. Our work may pave the way for explorations of replica wormhole physics in quantum simulators.