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

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.

5 pages + Supplemantal information, 1 figure version 3, accepted in Phys. Rev. Lett