Entanglement duality in spin-spin interactions

TL;DR

This paper explores how entanglement in thermal spin-1/2 dimers exhibits a duality related to spin-spin interactions, revealing topological features and classifications in the entanglement transition.

Contribution

It introduces a duality framework for entanglement transitions in spin dimers, linking symmetric and anti-symmetric classes with topological toric classifications.

Findings

Entanglement transition line is preserved across dual classes.

Dual categories of dimers are classified into toric entanglement classes.

Topological nature of entanglement is indicated by toric classification.

Abstract

We examine entanglement of thermal states for spin-12 dimers in external magnetic fields. Entanglement transition in the temperature-magnetic field plane demonstrates a duality in spin-spin interactions. This identifies dual categories of symmetric and anti-symmetric dimers with each category classified into toric entanglement classes. The entanglement transition line is preserved from each toric entanglement class to its dual toric class. The toric classification is an indication of topological nature of the entanglement.