We have recently revisited an old duality between the XY model and electrodynamics in d=2+1 dimensions derived by Fisher and Lee [1]. They showed that vortices behave like quantum particles with the Bose statistics. This old story, though, misses an important detail relevant to ferromagnets: the existence of vortex cores, where the XY model breaks down and one has to take the out-of-plane component into account. We did that [2] found that vortices can have Bose or Fermi statistics, depending on the spin Sz of the vortex core. Vortices with integer spin are bosons, those with half-integer spin are fermions. There is also a remote possibility of anyon statistics if the spin is neither integer nor half-integer.
[1] M. P. A. Fisher and D. H. Lee, "Correspondence between two-dimensional bosons and a bulk superconductor in a magnetic field," Phys. Rev. B 39, 2756 (1989)
[2] S. Dasgupta, S. Zhang, I. Bah, and O. Tchernyshyov, "Quantum statistics of vortices from a dual theory of the XY
ferromagnet," arXiv:1909.05248
Begin Flash video. (Or, right-click to download the 3gp file.)
Begin streaming QuickTime.
(Or, right-click to download the movie.)
Or [ Download the Podcast ].
Begin streaming RealMedia. (Or, right-click to download the audio file.)