Scaling of Entanglement Entropy for the Heisenberg Model on Clusters Joined by Point Contacts

TL;DR

This paper investigates how entanglement entropy scales in the Heisenberg model on clusters connected by a single bond, revealing deviations from the area law and showing linear scaling with system size.

Contribution

It provides computational analysis of entanglement entropy scaling in Heisenberg clusters joined by a single bond, highlighting deviations from the area law.

Findings

Entanglement entropy scales linearly with the number of sites or system size.

Both second Renyi and valence bond entropies increase with system size.

Scaling behavior differs from the traditional area law expectation.

Abstract

The scaling of entanglement entropy for the nearest neighbor antiferromagnetic Heisenberg spin model is studied computationally for clusters joined by a single bond. Bisecting the balanced three legged Bethe Cluster, gives a second Renyi entropy and the valence bond entropy which scales as the number of sites in the cluster. For the analogous situation with square clusters, i.e. two $L \times L$ clusters joined by a single bond, numerical results suggest that the second Renyi entropy and the valence bond entropy scales as $L$. For both systems, the environment and the system are connected by the single bond and interaction is short range. The entropy is not constant with system size as suggested by the area law.