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

• URL: http://arxiv.org/abs/2306.12571v1
• Date: Wed, 21 Jun 2023 21:15:24 GMT
• Title: Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Authors: Hanteng Wang, Chang Liu, Pengfei Zhang, Antonio M. Garc\'ia-Garc\'ia
• Abstract summary: Recent discoveries have highlighted the significance of replica wormholes in resolving the information paradox. We propose the dissipative Sachdev-Ye-Kitaev model (SYK) as a minimal quantum model that exhibits entanglement dynamics. We show that signature of replica wormholes persists even at moderate $N lesssim 30$ by using the Monte Carlo quantum trajectory method.
• Score: 7.050547368572957
• License: http://creativecommons.org/licenses/by/4.0/
• 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 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.

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