Quantum spin systems: toroidal classification and geometric duality

TL;DR

This paper introduces a classification and duality framework for quantum spin systems on a torus, revealing equivalences between ferromagnetic and antiferromagnetic materials and their quantum features, with implications for spintronics.

Contribution

It presents a novel toroidal classification and geometric duality for quantum spin systems, linking bipartite quantum features across magnetic regimes.

Findings

Antiferromagnetic regime acts as a dual to ferromagnetic regime.

Quantum correlations can be realized across ferro- and antiferromagnetic regimes.

Both regimes exhibit similar capabilities for quantum spintronics.

Abstract

Toroidal classification and geometric duality in quantum spin systems is presented. Through our classification and duality, we reveal that various bipartite quantum features in magnon-systems can manifest equivalently in both bipartite ferromagnetic and antiferromagnetic materials, based upon the availability of relevant Hamiltonian parameters. Additionally, the results highlight the antiferromagnetic regime as an ultra-fast dual counterpart to the ferromagnetic regime, both exhibiting identical capabilities for quantum spintronics and technological applications. Concrete illustrations are provided, demonstrating how splitting and squeezing types of two-mode magnon quantum correlations can be realized across ferro- and antiferromagnetic regimes.