Anyons in integer quantum Hall magnets

TL;DR

This paper demonstrates that in noncoplanar itinerant magnetic systems, magnetic vortices can carry fractional electronic quantum numbers and exhibit anyonic statistics, combining features of quantum Hall effects and magnetic textures.

Contribution

It introduces a novel mechanism for electronic fractionalization in magnetic systems with topologically nontrivial textures, supported by analytical and numerical analysis.

Findings

Magnetic vortices carry fractional (irrational) electronic quantum numbers.

Vortices exhibit Abelian anyonic statistics.

Analytical results are supported by extensive numerical calculations.

Abstract

Strongly correlated fractional quantum Hall liquids support fractional excitations, which can be understood in terms of adiabatic flux insertion arguments. A second route to fractionalization is through the coupling of weakly interacting electrons to topologically nontrivial backgrounds such as in polyacetylene. Here we demonstrate that electronic fractionalization combining features of both these mechanisms occurs in noncoplanar itinerant magnetic systems, where integer quantum Hall physics arises from the coupling of electrons to the magnetic background. The topologically stable magnetic vortices in such systems carry fractional (in general irrational) electronic quantum numbers and exhibit Abelian anyonic statistics. We analyze the properties of these topological defects by mapping the distortions of the magnetic texture onto effective non-Abelian vector potentials. We support our analytical results with extensive numerical calculations.