Supersymmetric Quantum Hall Effect on Fuzzy Supersphere

TL;DR

This paper constructs supersymmetric quantum Hall liquids on a supersphere, deriving a supersymmetric Laughlin wavefunction and exploring topological excitations with fractional charge.

Contribution

It introduces a supersymmetric generalization of the Laughlin wavefunction and analyzes topological excitations in supersymmetric quantum Hall systems.

Findings

Supersymmetric Laughlin wavefunction as ground state

Identification of fractionally charged topological excitations

Relations between quantum Hall systems and supersymmetric extensions

Abstract

Supersymmetric quantum Hall liquids are constructed on a supersphere in a supermonopole background. We derive a supersymmetric generalization of the Laughlin wavefunction, which is a ground state of a hard-core $OSp(1|2)$ invariant Hamiltonian. We also present excited topological objects, which are fractionally charged deficits made by super Hall currents. Several relations between quantum Hall systems and their supersymmetric extensions are discussed.