Replica wormhole and information retrieval in the SYK model coupled to Majorana chains

Abstract

Motivated by recent studies of the information paradox in (1+1)-D anti-de Sitter spacetime with a bath described by a (1+1)-D conformal field theory, we study the dynamics of second Ŕenyi entropy of the Sachdev-Ye-Kitaev (SYK) model (χ) coupled to a Majorana chain bath (ψ). The system is prepared in the thermofield double (TFD) state and then evolved by HL + HR. For small system-bath coupling, we find that the second Rényi entropy \( {S}_{\upchi L,\upchi R}^{(2)} \) of the SYK model undergoes a first order transition during the evolution. In the sense of holographic duality, the long-time solution corresponds to a “replica wormhole”. The transition time corresponds to the Page time of a black hole coupled to a thermal bath. We further study the information scrambling and retrieval by introducing a classical control bit, which controls whether or not we add a perturbation in the SYK system. The mutual information between the bath and the control bit shows a positive jump at the Page time, indicating that the entanglement wedge of the bath includes an island in the holographic bulk.

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Chen, Y., Qi, X. & Zhang, P. Replica wormhole and information retrieval in the SYK model coupled to Majorana chains. J. High Energ. Phys. 2020, 121 (2020). https://doi.org/10.1007/JHEP06(2020)121

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Keywords

  • 1/N Expansion
  • AdS-CFT Correspondence
  • 2D Gravity