Statistics of Quasiparticles in Fractional Quantum Hall States

TL;DR

This paper analyzes the statistics of quasiparticles in fractional quantum Hall states using chiral anomaly and Berry phase, deriving a generalized relation for their statistical phase and charge.

Contribution

It introduces a generalized relation for quasiparticle statistics and charge in FQH states based on topological and geometric analysis.

Findings

Statistical phase for quasiparticles at ν=p/q is e^{iπ p/q}.

Quasiholes have identical statistics to quasiparticles with opposite charge.

Charge of quasiparticles is -e p/q.

Abstract

We have considered here the statistics parameter for quasiparticles in FQH states from an analysis of these states in the framework of chiral anomaly and Berry phase. It is shown that we have a generalized relation such that the statistical phase of a quasiparticle for FQH states at $\nu=p/q$ with $p(q)$ even or odd, is given by $e^{i\pi \theta}$ with $\theta=p/q $ and the charge is $-e \frac{p}{q}$. The statistics parameter for a quasihole is identical with that of a quasiparticle and the charge is of opposite sign.