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

TL;DR

This paper demonstrates that a dissipative SYK model can exhibit entanglement dynamics similar to replica wormholes, including a first-order transition, providing a minimal quantum system to study these phenomena.

Contribution

We introduce a dissipative SYK model that shows entanglement features akin to replica wormholes, including a first-order transition and persistence at moderate system sizes.

Findings

Observation of a first-order entanglement transition in the dissipative SYK model.

Signature of replica wormholes persists at moderate system sizes (~30).

Potential for quantum simulation of replica wormhole physics.

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.