Holographic Entanglement Entropy of Multiple Strips

TL;DR

This paper analyzes holographic entanglement entropy for multiple strips across various geometries, revealing phase transitions and new minimal surface configurations, with implications for understanding entanglement structure in holographic theories.

Contribution

It classifies minimal surfaces for multiple strips, identifies phase transitions, and introduces new disconnected surface classes in confining geometries and black hole backgrounds.

Findings

Only 2 minimal surfaces for equal strips and separations.

Phase diagrams show first order geometric transitions.

New disconnected surfaces in confining geometries.

Abstract

We study holographic entanglement entropy (HEE) of $m$ strips in various holographic theories. We prove that for $m$ strips with equal lengths and equal separations, there are only 2 bulk minimal surfaces. For backgrounds which contain also "disconnected" surfaces, there are only 4 bulk minimal surfaces. Depending on the length of the strips and separation between them, the HEE exhibits first order "geometric" phase transitions between bulk minimal surfaces with different topologies. We study these different phases and display various phase diagrams. For confining geometries with $m$ strips, we find new classes of "disconnected" bulk minimal surfaces, and the resulting phase diagrams have a rich structure. We also study the "entanglement plateau" transition, where we consider the BTZ black hole in global coordinates with 2 strips. It is found that there are 4 bulk minimal surfaces, and the resulting phase diagram is displayed. We perform a general perturbative analysis of the $m$-strip system: including perturbing the CFT and perturbing the length or separation of the strips.