Intrinsic quasiparticle's spin and fractional quantum Hall effect on Riemann surfaces

TL;DR

This paper derives braid relations for charged anyons on Riemann surfaces, calculates their spin in fractional quantum Hall states, and finds the spin to be topologically invariant and physically consistent.

Contribution

It introduces a method to compute quasiparticle spin on Riemann surfaces using braid relations, highlighting topological invariance in fractional quantum Hall systems.

Findings

Quasiparticle spin is topologically independent.

Braid relations are derived for anyons on Riemann surfaces.

Spin satisfies physical restrictions.

Abstract

We derive the braid relations of the charged anyons interacting with a magnetic field on Riemann surfaces. The braid relations are used to calculate the quasiparticle's spin in the fractional quantum Hall states on Riemann surfaces. The quasiparticle's spin is found to be topological independent and satisfies physical restrictions.