Further Remarks on the Entanglement Entropy of Hopf links

TL;DR

This paper investigates the entanglement entropy of connected sums of Hopf links in three-dimensional space, revealing bounds, parity sensitivity, and potential limits as the number of components grows.

Contribution

It provides new insights into how entanglement entropy behaves in complex link configurations, including bounds and parity effects in $SU(2)$ theory.

Findings

Entanglement entropy has established lower and upper bounds.

$SU(2)$ theory shows sensitivity to link parity.

Possible existence of a limit for large numbers of link components.

Abstract

We study the connected sum of Hopf links in $S^3$. Particularly, we compute the entanglement entropy (EE) as a function of the number of link components. We find evidence of lower and upper bounds for the entanglement entropy. We show that the $SU(2)$ theory exhibits sensitivity to the parity of links. We also find evidence suggesting the existence of a well-defined limit of the large number of link components.