Ferromagnetism, antiferromagnetism, and the curious nematic phase of S=1 quantum spin systems

TL;DR

This paper explores the phase diagram of three-dimensional S=1 quantum spin systems, revealing ferromagnetic, antiferromagnetic, and nematic phases, and uses random loop representations to analyze symmetry breaking and pure states.

Contribution

It introduces a novel analysis of the nematic phase and symmetry breaking in S=1 quantum spin systems using random loop representations.

Findings

Confirmation of ferromagnetic and antiferromagnetic transitions

Identification of nematic pure states minimizing specific spin sums

Breaking of SU(3) invariance in the system

Abstract

We investigate the phase diagram of S=1 quantum spin systems with SU(2)-invariant interactions, at low temperatures and in three spatial dimensions. Symmetry breaking and the nature of pure states can be studied using random loop representations. The latter confirm the occurrence of ferro- and antiferromagnetic transitions and the breaking of SU(3) invariance. And they reveal the peculiar nature of the nematic pure states which MINIMIZE \sum_x (S_x^i)^2.