Entanglement Entropy of Annulus in Three Dimensions

TL;DR

This paper investigates the entanglement entropy of an annulus in three-dimensional systems, using numerical and holographic methods to analyze mutual information and phase behavior in gapped and gapless theories.

Contribution

It introduces a comprehensive analysis of minimal surfaces for annuli and classifies phase diagrams, revealing universal decay behavior of mutual information in gapped systems.

Findings

Mutual information decays exponentially with increasing gap scale.

Four types of minimal surface solutions are identified and classified.

Mutual information obeys monotonicity consistent with unitarity.

Abstract

The entanglement entropy of an annulus is examined in a three-dimensional system with or without a gap. For a free massive scalar field theory, we numerically calculate the mutual information across an annulus. We also study the holographic mutual information in the CGLP background describing a gapped field theory. We discover four types of solutions as the minimal surfaces for the annulus and classify the phase diagrams by varying the inner and outer radii. In both cases, we find the mutual information satisfies the monotonicity dictated by the unitarity and decays exponentially fast as the gap scale is increased. We speculate this is a universal behavior in any gapped system.