FRACTIONAL QUANTUM HALL EFFECT: CONSTRUCTION OF THE HARTREE–FOCK STATE BY USING TRANSLATIONAL COVARIANCE

Author:

FERRARI R.12

Affiliation:

1. Dipartimento di Fisica, Universitá di Trento 38050 Povo Trento, Italy

2. I.N.F.N., Sezione di Padova, Gruppo Collegato di Trento, Italy

Abstract

The formalism introduced in a previous paper is used for discussing the Coulomb interaction of many electrons moving in two space-dimensions in the presence of a strong magnetic field. The matrix element of the Coulomb interaction is evaluated in the new basis, whose states are invariant under discrete translations (up to a gauge transformation). This paper is devoted to the case of low filling factor, thus we limit ourselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor νf = 1/u we give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree–Fock equation. For general filling factor νf = u′/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. We generalize the Hartree–Fock equation by considering some correlation: all quantum states are allowed for the u′ electrons with the same translation quantum numbers. Numerical results are given for the mean energy and the energy bands, for some values of the filling factor (νf = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). Our results agree numerically with the Charge Density Wave approach. The boundary conditions are shown to be very important: only large systems (degeneracy of Landau level over 200) are not affected by the boundaries. Therefore results obtained on small scale systems are somewhat unreliable. The relevance of the results for the Fractional Quantum Hall Effect is briefly discussed.

Publisher

World Scientific Pub Co Pte Lt

Subject

Condensed Matter Physics,Statistical and Nonlinear Physics

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Multi-resolution analysis and fractional quantum Hall effect: more results;Journal of Physics A: Mathematical and General;2002-12-12

2. Compressible anisotropic states around the half-filled Landau levels;Physical Review B;2000-02-15

3. Field theory on the von Neumann lattice and the quantized Hall conductance of Bloch electrons;Physica E: Low-dimensional Systems and Nanostructures;1999-01

4. Floquet Energies and Quantum Hall Effect in a Periodic Potential;International Journal of Modern Physics B;1998-05-10

5. On the Collective Mode Spectrum in FQHE;International Journal of Modern Physics B;1998-05-10

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