Fractional Spin for Quantum Hall Effect Quasiparticles

TL;DR

This paper explores whether quasiparticles in the fractional quantum Hall effect have fractional intrinsic spin, revealing two contributions to spin and confirming a generalized spin-statistics relation on a sphere.

Contribution

It provides a detailed Berry-phase analysis showing two distinct spin contributions for quasiparticles and confirms the spin-statistics relation in the fractional quantum Hall context.

Findings

Two spin contributions identified: self-interaction and kinematical effects.

Total spin satisfies the generalized spin-statistics theorem.

No corresponding spin terms found on the plane.

Abstract

We investigate the issue of whether quasiparticles in the fractional quantum Hall effect possess a fractional intrinsic spin. The presence of such a spin $S$ is suggested by the spin-statistics relation $S=\theta/2\pi$, with $\theta$ being the statistical angle, and, on a sphere, is required for consistent quantization of one or more quasiparticles. By performing Berry-phase calculations for quasiparticles on a sphere we find that there are two terms, of different origin, that couple to the curvature and can be interpreted as parts of the quasiparticle spin. One, due to self-interaction, has the same value for both the quasihole and quasielectron, and fulfills the spin-statistics relation. The other is a kinematical effect and has opposite signs for the quasihole and quasielectron. The total spin thus agrees with a generalized spin-statistics theorem $(S_{qh} + S_{qe})/2 = \theta/2\pi$. On the plane, we do not find any corresponding terms.