Entanglement Phase Structure of a Holographic BCFT in a Black Hole Background

TL;DR

This paper explores the entanglement phase structure of a holographic BCFT in a black hole background, revealing novel island formations and phase behaviors at finite temperature.

Contribution

It demonstrates the existence of entanglement islands below a critical angle at finite temperature, extending previous zero-temperature results.

Findings

Entanglement islands exist below the critical angle at finite temperature.

The entanglement entropy exhibits either constant or Page curve behavior depending on parameters.

The phase structure includes a finite connected region called the atoll.

Abstract

We compute holographic entanglement entropy for subregions of a BCFT thermal state living on a nongravitating black hole background. The system we consider is doubly holographic and dual to an eternal black string with an embedded Karch-Randall brane that is parameterized by its angle. Entanglement islands are conventionally expected to emerge at late times to preserve unitarity at finite temperature, but recent calculations at zero temperature have shown such islands do not exist when the brane lies below a critical angle. When working at finite temperature in the context of a black string, we find that islands exist even when the brane lies below the critical angle. We note that although these islands exist when they are needed to preserve unitarity, they are restricted to a finite connected region on the brane which we call the atoll. Depending on two parameters -- the size of the subregion and the brane angle -- the entanglement entropy either remains constant in time or follows a Page curve. We discuss this rich phase structure in the context of bulk reconstruction.