Berry phases for composite fermions: effective magnetic field and fractional statistics

TL;DR

This paper calculates the Berry phase and fractional statistics of composite fermion quasiparticles in quantum Hall systems, confirming their fractional statistics and analyzing corrections due to wave function overlap.

Contribution

It provides a quantitative computation of Berry phases for composite fermion quasiparticles, supporting fractional statistics theory with considerations of overlap corrections.

Findings

Berry phase agrees with effective magnetic field concept

Supports the validity of fractional statistics in quantum Hall superfluids

Identifies corrections to fractional statistics due to wave function overlap

Abstract

The quantum Hall superfluid is presently the only viable candidate for a realization of quasiparticles with fractional Berry phase statistics. For a simple vortex excitation, relevant for a subset of fractional Hall states considered by Laughlin, non-trivial Berry phase statistics were demonstrated many years ago by Arovas, Schrieffer, and Wilczek. The quasiparticles are in general more complicated, described accurately in terms of excited composite fermions. We use the method developed by Kjonsberg, Myrheim and Leinaas to compute the Berry phase for a single composite-fermion quasiparticle, and find that it agrees with the effective magnetic field concept for composite fermions. We then evaluate the "fractional statistics", related to the change in the Berry phase for a closed loop caused by the insertion of another composite-fermion quasiparticle in the interior. Our results support the general validity of fractional statistics in the quantum Hall superfluid, while also giving a quantitative account of corrections to it when the quasiparticle wave functions overlap. Many caveats, both practical and conceptual, are mentioned that will be relevant to an experimental measurement of the fractional statistics. A short report on some parts of this article has appeared previously.