Fractional quantum Hall effect: Construction of the Hartree-Fock state by using translational covariance
- Univ. di Trento (Italy). Dipt. di Fisica I.N.F.N., Trento (Italy). Gruppo Collegato
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. This paper is devoted to the case of low filling factor, thus the authors limit themselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor [nu][sub f] = 1/u they give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree-Fock equation. For general filling factor [nu][sub f] = u[prime]/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. They generalize the Hartree-Fock equation by considering some correlation: all quantum states are allowed for the u[prime] 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 ([nu][sub f] = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). The 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.
- OSTI ID:
- 6971319
- Journal Information:
- International Journal of Modern Physics B; (United States), Journal Name: International Journal of Modern Physics B; (United States) Vol. 8:5; ISSN IJPBEV; ISSN 0217-9792
- Country of Publication:
- United States
- Language:
- English
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