Spin vortices, skyrmions and the Kosterlitz-Thouless transition in the two-dimensional antiferromagnet

TL;DR

This paper explores spin-vortex excitations in 2D antiferromagnets using nonlinear sigma models, revealing a Kosterlitz-Thouless transition from a plasma to a molecular phase influenced by instanton behavior.

Contribution

It extends the instanton gas picture from 2D to (2+1)D nonlinear sigma models, demonstrating a phase transition in the spin-vortex system.

Findings

Identification of instanton solutions as skyrmions in the model

Mapping quantum fluctuations to a Coulomb gas framework

Prediction of a Kosterlitz-Thouless transition at finite temperature

Abstract

We investigate spin-vortex excitations in the two-dimensional antiferromagnet on the basis of the nonlinear sigma model. The model of two-dimensional Heisenberg quantum antiferromagnet is mapped onto the (2+1)D nonlinear sigma model. The 2D nonlinear sigma model has an instanton (or skyrmion) solution which describes an excitation of spin-vortex type. Quantum fluctuations of instantons are reduced to the study of the Coulomb gas, and the gas of instantons of the 2D nonlinear sigma model is in the plasma phase. We generalize this picture of instanton gas to the (2+1)D nonlinear sigma model. We show, using some approximation, that there is a Kosterlitz-Thouless transition from the plasma phase to the molecular phase as the temperature is lowered.