Measurable fractional spin for quantum Hall quasiparticles on the disk

TL;DR

This paper introduces a measurable fractional spin for quantum Hall quasiparticles on a disk, linking it to their topological properties and quadrupole moments, offering a new way to detect anyonic behavior experimentally.

Contribution

It defines a measurable fractional spin for quantum Hall quasiparticles that satisfies the spin-statistics relation and relates to their quadrupole moments, advancing topological phase understanding.

Findings

The proposed spin satisfies the spin-statistics relation.

The spin can be experimentally measured via quadrupole moments.

Numerical and analytical studies confirm the spin's properties for Laughlin and Halperin states.

Abstract

We study the spin of the localised quasiparticle excitations of lowest-Landau-level quantum Hall states defined on a disk. The spin that we propose satisfies the spin-statistics relation and can be used to reconstruct the topological geometric phase associated to the exchange of two arbitrarily chosen quasiparticles. Since it is related to the quadrupole moment of the quasiparticle charge distribution, it can be measured in an experiment and could reveal anyonic properties in a way that is complementary to the interferometric schemes employed so far. We first discuss our definition for the quasiholes of the Laughlin state, for which we present a numerical and analytical study of our spin, and we proceed with a discussion of several kinds of quasiholes of the Halperin 221 state. Finally, we discuss the link between our spin and the adiabatic rotation of the quasiparticles around their axis and demonstrate that our spin obeys the spin-statistics relation.