Landau Levels and Quantum Group

TL;DR

This paper uncovers a quantum group symmetry in the Landau level problem of electrons in magnetic fields, linking the algebra's deformation parameter to the fractional quantum Hall filling factor.

Contribution

It reveals a quantum group structure underlying Landau levels and connects the deformation parameter to fractional filling factors, offering new insights into quantum Hall systems.

Findings

Quantum group symmetry commutes with the Hamiltonian.

Deformation parameter q relates to fractional filling factor /m.

Wavefunctions form the basis of the quantum algebra.

Abstract

We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wavefunctions of the system. The quantum group symmetry commutes with the Hamiltonian and is relevant to the Landau level degeneracy. The deformation parameter $q$ of the quantum algebra turns out to be given by the fractional filling factor $\nu=1/m$ ($m$ odd integer).