On the relation between fractional charge and statistics

TL;DR

This paper clarifies the fundamental link between fractional charge and fractional statistics, resolving previous contradictions and establishing the necessity of their relation through anomaly arguments in quantum Hall systems.

Contribution

It revisits and corrects a classic argument connecting fractional charge and statistics, introducing a new anomaly-based proof for Laughlin states.

Findings

Resolved a contradiction in the original charge-statistics argument

Established the necessity of the charge-statistics relation via anomaly analysis

Provided a clearer theoretical foundation for fractional quantum Hall states

Abstract

We revisit an argument, originally given by Kivelson and Ro\v{c}ek, for why the existence of fractional charge necessarily implies fractional statistics. In doing so, we resolve a contradiction in the original argument, and in the case of a $\nu = 1/m$ Laughlin holes, we also show that the standard relation between fractional charge and statistics is necessary by an argument based on a t'Hooft anomaly in a global one-form ${\mathcal Z}_m$ symmetry.