Many Particle Hamiltonian for the Fractional Quantum Hall Effect

TL;DR

This paper proposes a many-particle Hamiltonian model to explain the fractional quantum Hall effect, linking quasi-particle spectra and degeneracies to fractional filling factors and experimental observations.

Contribution

It introduces a novel many-particle Hamiltonian framework that connects magnetic field, electron density, and fractional filling factors to FQHE phenomena.

Findings

Quasi-particle energy gaps align with experimental data

Degeneracies correspond to fractional filling factors

FQH conductance characterized as a topological invariant

Abstract

A many-particle Hamiltonian is proposed in order to explain the fractional quantum Hall effect (FQHE) for fractional filling factors $\nu < 1$. The solutions of the corresponding Hartree-Fock equations make it possible to discuss the FQHE from the point of view of the single quasi-particle energy spectrum. It is shown how the specific couplings in the many-particle Hamiltonian depend on the magnetic field and the area density of electrons. The degeneracies of the quasi-particle states are related to the fractional filling factors $\nu$. It is suggested that the energy gaps obtained in the quasi-particle energy spectrum are comparable with the experimentally measured quantities. An explicit calculation for the FQH - conductance is given and its character as a topological invariant is discussed.