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arXiv · 2011.09622

Perturbative calculations of entanglement entropy

Pouria Dadras·Alexei Kitaev
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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.

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Pouria Dadras, Alexei Kitaev. 2020-11-19. Perturbative calculations of entanglement entropy. https://doi.org/10.1007/jhep03(2021)198

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