Perturbative calculations of entanglement entropy

Abstract

This paper is an attempt to extend the recent understanding of the Page curve for evaporating black holes to more general systems coupled to a heat bath. Although calculating the von Neumann entropy by the replica trick is usually a challenge, we have identified two solvable cases. For the initial section of the Page curve, we sum up the perturbation series in the system-bath coupling $\kappa$; the most interesting contribution is of order $2s$, where $s$ is the number of replicas. For the saturated regime, we consider the effect of an external impulse on the entropy at a later time and relate it to OTOCs. A significant simplification occurs in the maximal chaos case such that the effect may be interpreted in terms of an intermediate object, analogous to the branching surface of a replica wormhole.

17 pages, 7 figures, fixing an error in section 3.5 has lead to a much simpler result. An alternative, shorter derivation is given. (new contributions by a new author, Pengfei Zhang.)

References in corpus (2)

• Black holes as mirrors: quantum information in random subsystems
• Spread of entanglement in a Sachdev-Ye-Kitaev chain

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• Page Curve from Non-Markovianity
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Entropy Linear Response Theory with Non-Markovian Bath
• Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos