Perturbative calculations of entanglement entropy

TL;DR

This paper develops perturbative methods to compute entanglement entropy in complex quantum systems, extending the understanding of the Page curve for black holes to more general coupled systems, and explores the effects of external impulses and chaos.

Contribution

It introduces solvable perturbative approaches for entanglement entropy calculations in coupled systems and relates entropy dynamics to chaos and replica wormholes.

Findings

Perturbation series summed for initial Page curve segment.

External impulses affect entropy, linked to OTOCs.

Maximal chaos simplifies entropy effects, akin to replica wormholes.

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.