Many Particle Hamiltonian for the Fractional Quantum Hall Effect

Details Many Particle Hamiltonian for the Fractional Quantum Hall Effect Many Particle Hamiltonian for the Fractional Quantum Hall Effect

1993-02-19

arxiv.org/abs/cond-mat/9302032v1

Physics

Condensed Matter

24 pages, 4 figures available from lois@control, Latex, EFI 92-47

Scientific paper

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.

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