[Seminar] Quantum statistics of magnetic vortices

Speaker

Prof. Oleg Tchernyshyov - Johns Hopkins University
Oleg Tchernyshyov is a condensed matter theorist interested in all kinds of magnetic materials, from the familiar iron ferromagnets to spin ice to quantum and classical spin liquids.

Title

Quantum statistics of magnetic vortices

Abstract

We have recently revisited an old duality between the XY model and electromagnetism originally derived in d=2 dimensions by Kosterlitz [1] and extended to d=2+1 by Fisher and Lee [2]. According to this duality, vortices behave like bosons with an electric charge equal to the vortex winding number. The old story, however, missed an important detail: the existence of vortex cores, where magnetization points normally to the easy plane and the XY model breaks down. Our reexamination of the duality [3] has revealed that vortices are mapped onto particles carrying not only an electric charge but also a magnetic flux equal to the net spin Sz of the vortex core. Wilczek showed that such particles may alter their quantum statistics [4]. Therefore, vortices with integer spin are bosons, whereas those with half-integer spin are fermions.

[1] J. M. Kosterlitz, "The critical properties of the two-dimensional xy model," J. Phys. C 7, 1046 (1974).
[2] 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).
[3] S. Dasgupta, S. Zhang, I. Bah, and O. Tchernyshyov, "Quantum statistics of vortices from a dual theory of the XY ferromagnet," Phys. Rev. Lett. 124, 157203 (2019).
[4] F. Wilczek, "Magnetic flux, angular momentum, and statistics," Phys. Rev. Lett. 48, 1144 (1982).

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