Fractional statistics in the fractional quantum Hall effect

TL;DR

This paper provides a microscopic calculation confirming the fractional statistics of quasiparticles in the fractional quantum Hall effect by evaluating the Berry phase for composite-fermion quasiparticles at specific filling factors.

Contribution

It offers the first microscopic verification of fractional statistics in the fractional quantum Hall effect through Berry phase calculations.

Findings

Confirmed fractional statistics of quasiparticles at ν=1/3 and ν=2/5

Highlighted the importance of trajectory perturbations in calculations

Discussed conditions for the applicability of fractional statistics

Abstract

A microscopic confirmation of the fractional statistics of the {\em quasiparticles} in the fractional quantum Hall effect has so far been lacking. We calculate the statistics of the composite-fermion quasiparticles at $\nu=1/3$ and $\nu=2/5$ by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. A careful consideration of subtle perturbations in the trajectory due to the presence of an additional quasiparticle is crucial for obtaining the correct value of the statistics. The conditions for the applicability of the fractional statistics concept are discussed.