A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices

TL;DR

This paper employs group theoretical methods to unify the description of antiferromagnetic Heisenberg spins on various low-dimensional lattices, revealing a common SO3 order parameter interacting with a local gauge field.

Contribution

It introduces a universal framework using group theory that describes antiferromagnetic order parameters as elements of SO3, extending the spin group with a local gauge field for different lattice types.

Findings

Order parameter lives on SO3 for triangular and square lattices

Interactions involve a local gauge field rather than a global one

Recovers Haldane decomposition for antiferromagnetic chain

Abstract

Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice. For the antiferromagnetic chain we recover the Haldane decomposition. This order parameter interacts with a local gauge field rather than with a global one as implicitly suggested in the literature which in our approach appears in a rather natural manner. In fact this merely corresponds to a novel extension of the spin group by a local gauge field. This analysis based on the real division algebras applies to low dimensional lattices.