Singlets and reflection symmetric spin systems

TL;DR

This paper proves exact properties of reflection symmetric antiferromagnetic spin systems with crossing bonds, showing at least one ground state has zero total spin and a positive semidefinite coefficient matrix, extending previous bipartite results.

Contribution

It extends known results to non-bipartite, frustrated spin systems with crossing bonds, establishing ground state properties under reflection symmetry.

Findings

At least one ground state has total spin zero.

The coefficient matrix of the ground state is positive semidefinite.

Results apply to frustrated spin systems with crossing bonds.

Abstract

We rigorously establish some exact properties of reflection symmetric spin systems with antiferromagnetic crossing bonds: At least one ground state has total spin zero and a positive semidefinite coefficient matrix. The crossing bonds obey an ice rule. This augments some previous results which were limited to bipartite spin systems and is of particular interest for frustrated spin systems.