A Super-Flag Landau Model

TL;DR

This paper develops an exactly solvable super-flag Landau model describing a quantum particle on a superspace, revealing finite-dimensional Hilbert spaces and special wavefunction properties tied to supersymmetry and topological terms.

Contribution

It introduces a super-generalization of the Landau model on a super-flag manifold, incorporating Wess-Zumino terms, and solves it exactly using the factorization method, highlighting finite-dimensional Hilbert spaces.

Findings

Finite-dimensional Hilbert space due to bounded Landau levels

Wavefunctions in degenerate irreps of SU(2|1)

Exact solvability via the factorization method

Abstract

We consider the quantum mechanics of a particle on the coset superspace $SU(2|1)/[U(1)\times U(1)]$, which is a super-flag manifold with $SU(2)/U(1)\cong S^2$ `body'. By incorporating the Wess-Zumino terms associated with the $U(1)\times U(1)$ stability group, we obtain an exactly solvable super-generalization of the Landau model for a charged particle on the sphere. We solve this model using the factorization method. Remarkably, the physical Hilbert space is finite-dimensional because the number of admissible Landau levels is bounded by a combination of the U(1) charges. The level saturating the bound has a wavefunction in a shortened, degenerate, irrep of $SU(2|1)$.