The SU(2) $\times$ SU(2) chiral spin model in terms of SO(3) and Z$_2$ variables: vortices and disorder

TL;DR

This paper reformulates the 2D SU(2)×SU(2) chiral spin model using SO(3) and Z2 variables, revealing the significance of vortices and strings in the system's disordering process at low temperatures.

Contribution

It introduces a novel representation of the model in terms of SO(3) and Z2 degrees of freedom, highlighting the role of vortices and strings in its disordering mechanism.

Findings

Dynamical SO(3) vortices and strings are identified in the model.

Vortices with long strings are crucial for disordering at low temperatures.

The reformulation provides insight into topological excitations in the spin system.

Abstract

We rewrite the two-dimensional SU(2)$\times$ SU(2) chiral spin model in terms of SO(3) and {\bf Z}$_2$ degrees of freedom. The transformation, which is motivated by a similar representation of the corresponding lattice gauge theory in higher dimensions, exhibits the presence of dynamical SO(3) vortices and associated strings. We present arguments that (pairs of) SO(3) vortices with long strings play a crucial role in disordering the spin system at arbitrarily low temperatures.