Hyperspherical Slater determinant approach to few-body fractional quantum Hall states

TL;DR

This paper enhances the hyperspherical approach for few-body fractional quantum Hall states by integrating Slater determinants, improving computational efficiency and establishing a link with the traditional single-particle framework.

Contribution

It introduces a Slater determinant-based hyperspherical basis, overcoming previous symmetrization limitations and connecting hyperspherical and single-particle descriptions.

Findings

Improved computational efficiency in hyperspherical calculations.

Established a clear connection between hyperspherical and single-particle frameworks.

Provided a compact operator representation of the theoretical model.

Abstract

In a recent study[Phys. Rev. B 92 (2015) 125427], a hyperspherical approach has been developed to study of few-body fractional quantum Hall states. This method has been successfully applied to the exploration of few boson and fermion problems in the quantum Hall region, as well as the study of inter-Landau level collective excitations. However, the hyperspherical method as it is normally implemented requires a subsidiary (anti-)symmetrization process, which limits its computational effectiveness. The present work overcomes these difficulties and extends the power of this method by implementing a represen- tation of the hyperspherical many-body basis space in terms of Slater determinants of single particle eigenfunctions. A clear connection between the hyperspherical representation and the conventional single particle picture is presented, along with a compact operator representation of the theoretical framework.