Mutual statistics, braid group, and the fractional quantum Hall effect

TL;DR

This paper explores how mutual statistics emerge from braid group representations and models the bilayered fractional quantum Hall effect, demonstrating fractional mutual statistics of quasiholes and proposing a 3D FQHE model.

Contribution

It introduces a braid group-based framework for mutual statistics and presents a Hamiltonian model for bilayered FQHE with fractional mutual statistics.

Findings

Quasiholes exhibit fractional mutual statistics.

A Hamiltonian model for bilayered FQHE is proposed.

A 3D FQHE model using multi-layered samples is suggested.

Abstract

We show that the notion of mutual statistics arises naturally from the representation theory of the braid group over the multi-sheeted surface. A Hamiltonian which describes particles moving on the double-sheeted surface is proposed as a model for the bilayered fractional quantum Hall effect (FQHE) discovered recently. We explicitly show that the quasi-holes of the bilayered Hall fluid display fractional mutual statistics. A model for 3-dimensional FQHE using the multi-layered sample is suggested.