On the relation between fractional charge and statistics

TL;DR

This paper reassesses the Kivelson-Roček argument that fractional charge implies fractional statistics and resolves a prior inconsistency. It demonstrates that, for Laughlin-type states, the charge–statistics relation is enforced by a global one-form symmetry and a corresponding t'Hooft anomaly. Using BF and Chern-Simons formulations, the authors show that flux-threading arguments require a compensating statistical phase, yielding an exchange phase tied to the fractional charge. The work extends to general filling fractions and reinforces a spin-statistics connection for anyons, linking fractional charge, fractional statistics, and topological anomalies in topological quantum matter.

Abstract

We revisit an argument, originally given by Kivelson and Roček, 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 $ν= 1/m$ 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.