Large distance expansion of Mutual Information for disjoint disks in a free scalar theory

TL;DR

This paper calculates the next-to-leading order term in the long-distance expansion of mutual information between two disjoint disks in a free scalar theory in three dimensions, finding no non-analyticity in the Rényi parameter.

Contribution

It provides the first detailed computation of the next-to-leading order mutual information term for disjoint disks in a free scalar field in three dimensions.

Findings

Next-to-leading order term computed for the mutual information.

No evidence of non-analyticity in the Rényi parameter n.

Results extend understanding of entanglement in free scalar theories.

Abstract

We compute the next-to-leading order term in the long-distance expansion of the mutual information for free scalars in three space-time dimensions. The geometry considered is two disjoint disks separated by a distance $r$ between their centers. No evidence for non-analyticity in the R\'enyi parameter $n$ for the continuation $n \rightarrow 1$ in the next-to-leading order term is found.