Islands, Double Holography, and the Entanglement Membrane

TL;DR

This paper establishes a quantitative link between semi-classical gravity calculations of the Page curve using quantum extremal islands and the entanglement membrane model describing entanglement dynamics in chaotic quantum systems.

Contribution

It demonstrates that entanglement dynamics in a double-holographic black hole model are accurately described by the entanglement membrane, connecting gravity and quantum many-body physics.

Findings

Entanglement dynamics match the entanglement membrane description.

The Page curve can be computed via the entanglement membrane in the holographic model.

A quantitative equivalence between gravity and quantum chaos calculations is established.

Abstract

The quantum extremal island rule allows us to compute the Page curves of Hawking radiation in semi-classical gravity. In this work, we study the connection between these calculations and the thermalisation of chaotic quantum many-body systems, using a coarse-grained description of entanglement dynamics known as the entanglement membrane. Starting from a double-holographic model of eternal two-sided asymptotically AdS$_d$ ($d>2$) black hole each coupled to a flat $d$-dimensional bath, we show that the entanglement dynamics in the late-time, large-subregion limit is described by entanglement membrane, thereby establishing a quantitative equivalence between a semi-classical gravity and a chaotic quantum many-body system calculation of the Page curve.