Replica wormhole and information retrieval in the SYK model coupled to Majorana chains
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 $$S^(2)_{χL,χR}$$ 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.
- Research Organization:
- University of California, Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); Simons Foundation
- Grant/Contract Number:
- SC0019380; 1720504
- OSTI ID:
- 1646615
- Journal Information:
- Journal of High Energy Physics (Online), Vol. 2020, Issue 6; ISSN 1029-8479
- Publisher:
- Springer NatureCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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