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

Journal Article · Fri Jun 19 00:00:00 EDT 2020 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP06(2020)121· OSTI ID:1646615

Chen, Yiming ^[1]; Qi, Xiao-Liang ^[2]; Zhang, Pengfei ^[3]

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1. Princeton Univ., NJ (United States); OSTI
2. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics and Dept. of Physics
3. California Institute of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics and Inst. for Quantum Information and Matter

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: Univ. of California, Berkeley, CA (United States)
• Sponsoring Organization: National Science Foundation (NSF); Simons Foundation; USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0019380
• OSTI ID: 1646615
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 6 Vol. 2020; ISSN 1029-8479
• Publisher: Springer Nature
• Country of Publication: United States
• Language: English

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