Quantum Hall Liquid on a Noncommutative Superplane

TL;DR

This paper constructs supersymmetric quantum Hall liquids on a noncommutative superplane, revealing superpartner states and topological features, and discusses their relation to bilayer quantum Hall systems.

Contribution

It introduces a supersymmetric formalism for the Landau problem on a noncommutative superplane, highlighting superpartner wavefunctions and topological excitations.

Findings

Existence of superpartner states for Laughlin wavefunctions

Super-chiral property of states in the lowest Landau level

Analogies between supersymmetric quantum Hall systems and bilayer systems

Abstract

Supersymmetric quantum Hall liquids are constructed on a noncommutative superplane. We explore a supersymmetric formalism of the Landau problem. In the lowest Landau level, there appear spin-less bosonic states and spin-1/2 down fermionic states, which exhibit a super-chiral property. It is shown the Laughlin wavefunction and topological excitations have their superpartners. Similarities between supersymmetric quantum Hall systems and bilayer quantum Hall systems are discussed.