Replica wormhole and information retrieval in the SYK model coupled to Majorana chains
Yiming Chen, Xiao-Liang Qi, Pengfei Zhang
Abstract
A bstract 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 H L + H R . For small system-bath coupling, we find that the second Rényi entropy $$ {S}_{\upchi L,\upchi R}^{(2)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mrow> <mml:mi>χ</mml:mi> <mml:mi>L</mml:mi> <mml:mo>,</mml:mo> <mml:mi>χ</mml:mi> <mml:mi>R</mml:mi> </mml:mrow> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> </mml:msubsup> </mml:math> 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.