Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry

TL;DR

This paper numerically demonstrates that composite fermion particles in fractional quantum Hall states exhibit Abelian fractional statistics using spherical geometry, providing a clearer method than previous disk geometry approaches.

Contribution

The study introduces a more transparent numerical method to determine fractional statistics of composite fermions in FQH states using spherical geometry.

Findings

Confirmed Abelian fractional statistics of CFPs in spherical geometry

Circumvented phase shift issues present in disk geometry

Method applicable to non-Abelian FQH quasiparticles

Abstract

Fractional quantum Hall (FQH) fluids host quasiparticle excitations that carry a fraction of the electronic charge. Moreover, in contrast to bosons and fermions that carry exchange statistics of $0$ and $\pi$ respectively, these quasiparticles of FQH fluids, when braided around one another, can accumulate a Berry phase, which is a fractional multiple of $\pi$. Deploying the spherical geometry, we numerically demonstrate that composite fermion particle (CFP) excitations in the Jain FQH states carry Abelian fractional statistics. Previously, the exchange statistics of CFPs were studied in the disk geometry, where the statistics get obscured due to a shift in the phase arising from the addition of another CFP, making its determination cumbersome without prior knowledge of the shift. We show that on the sphere this technical issue can be circumvented and the statistics of CFPs can be obtained more transparently. The ideas we present can be extended to determine the statistics of quasiparticles arising in certain non-Abelian partonic FQH states.