Spin fractionalization at the edge of quantum Hall fluids induced by bulk quasiparticles

TL;DR

This paper introduces a measurable fractional spin at the edge of quantum Hall states influenced by bulk quasiparticles, providing a geometric framework applicable to various shapes and supported by numerical simulations.

Contribution

It defines a measurable edge spin in quantum Hall states affected by bulk quasiparticles, independent of global symmetries, and supports it with numerical calculations.

Findings

Edge spin takes fractional values inherited from bulk quasiparticles.

The geometric picture applies to different edge and quasiparticle shapes.

Numerical results confirm the fractional edge spin in specific quantum Hall states.

Abstract

We define a measurable spin for the edge of a lowest Landau level and incompressible fractional quantum Hall state in the presence of an Abelian or non-Abelian bulk quasiparticle. We show that this quantity takes a fractional value inherited from the fractional spin of the bulk quasiparticle. We present a geometric picture that does not rely on global symmetries of the wavefunction but is able to treat quasiparticles and edges with different shapes. We study finite-size many-body wavefunctions on the cylinder with circular quasiparticles and straight edges. Our results are supported by matrix-product-state calculations for the Laughlin and the k=3 Read-Rezayi states.