Hierarchical Wave Functions and Fractional Statistics in Fractional Quantum Hall Effect on the Torus

TL;DR

This paper constructs hierarchical wave functions for the fractional quantum Hall effect on a torus, clarifying the multi-component structure, degeneracy, and fractional statistics of quasiparticles, aligning with braid group analysis.

Contribution

It introduces a new class of hierarchical wave functions for FQHE on the torus, elucidating their multi-component nature and fractional statistics.

Findings

Wave functions reflect multi-component structure and degeneracy.

Quasiparticle braid statistics match anyon interactions on the torus.

Results support the braid group analysis of fractional statistics.

Abstract

One kind of hierarchical wave functions of Fractional Quantum Hall Effect (FQHE) on the torus are constructed. The multi-component nature of anyon wave functions and the degeneracy of FQHE on the torus are very clear reflected in this kind of wave functions. We also calculate the braid statistics of the quasiparticles in FQHE on the torus and show they fit to the picture of anyons interacting with magnetic field on the torus obtained from braid group analysis.