Quantum statistics of vortices from a dual theory of the XY ferromagnet

TL;DR

This paper develops a dual theory for the quantum behavior of vortices in XY ferromagnets, revealing their charge, flux, and fermionic nature, and extends classical mappings to include quantum and dynamical effects.

Contribution

It introduces a quantum dual theory for vortices in XY ferromagnets, incorporating dynamical phenomena and revealing their quantum statistics and properties.

Findings

Vortices behave as quantum particles with specific charge and flux.

Half-integer core spin vortices exhibit fermionic statistics.

The classical duality is extended to include quantum and dynamical effects.

Abstract

We extend the well-known mapping between the easy-plane ferromagnet and electrostatics in $d=2$ spatial dimensions to dynamical and quantum phenomena in a $d=2+1$ spacetime. Ferromagnetic vortices behave like quantum particles with an electric charge equal to the vortex number and a magnetic flux equal to the transverse spin of the vortex core. Vortices with half-integer core spin exhibit fermionic statistics.