Laughlin states and their quasi-particle excitations on the torus

TL;DR

This paper derives Laughlin's wave functions for quantum Hall states on a torus, including challenging quasi-electron excitations, using an operator formalism to address an open problem from prior research.

Contribution

It provides a complete derivation of Laughlin states and their quasi-particle excitations on a torus, including the quasi-electron, using an operator approach.

Findings

Derivation of Laughlin wave functions on a torus

Inclusion of quasi-electron excitations

Resolution of an open problem from Haldane and Rezayi

Abstract

We provide a full derivation of Laughlin's Jastrow-type wave functions for quantized Hall states subject to periodic boundary conditions using an operator formalism. The construction includes the quasi-hole and the technically more challenging quasi-electron excitation, which was left as an open problem in the classic paper by Haldane and Rezayi [Phys. Rev. B 31, 2529 (1985)].