Quantum Group Symmetry and Quantum Hall Wavefunctions on a Torus

TL;DR

This paper uncovers a quantum group symmetry in the behavior of electrons in a magnetic field on a torus, linking it to quantum Hall wavefunctions and the filling factor, revealing new algebraic structures in quantum Hall systems.

Contribution

It demonstrates a quantum group structure underlying quantum Hall wavefunctions on a torus, connecting algebraic symmetry to physical degeneracies and filling factors.

Findings

Quantum group symmetry is present in 2D electron motion on a torus.

The basis of the quantum algebra matches Haldane-Rezayi wavefunctions.

The deformation parameter equals the Landau-level filling factor.

Abstract

We find a quantum group structure in two-dimensional motion of nonrelativistic electrons in a uniform magnetic field on a torus. The representation basis of the quantum algebra is composed of the quantum Hall wavefunctions proposed by Haldane-Rezayi at the Landau-level filling factor $\nu=1/m$ ($m$ odd). It is also shown that the quantum group symmetry is relevant to the degenerate Landau states and the deformation parameter of the quantum algebra is given by the filling factor.