Calculations For Finite Systems Research Articles

Spin-reversed Quasiparticles in the Fractional Quantum Hall Effect - Finite System Calculations

The elementary charged excitations at 1/3 Landau level filling have been studied for various spin polarizations for finite electron systems in a periodic rectangular geometry. In the absence of Zeeman energy, the spin-reversed excitations, studied for three to six electron systems show significant reduction of the energy gap, compared to the fully spin-polarized quasiparticle-quasihole gap, studied for upto seven electron systems. In the presence of Zeeman energy, the lowest energy excitations involve spin-reversed quasiparticles and spin-polarized quasiholes for low magnetic fields. With increasing magnetic fields, a crossover point is reached (in the region B < 10 T), beyond which a fully spin polarized quasiparticle-quasihole state will be energetically favored. The Zeeman energy due to spin-flip explains qualitatively the linear magnetic field dependence of the activation energies observed experimentally.

Exchange- and Correlation-Energy Calculations in Finite Systems

In the local-effective-potential approximation of the Kohn-Sham self-consistent scheme applied to an atomic system, it was reported that while the calculated exchange energies for various atoms were accurate to within 10%, the correlation energies of atoms were too large by a factor of 2. A model system is set up to study the reason why the exchange energy estimates are so much better than those of the correlation energy even though they were treated on the same footing. It was found that, in using expressions derived from an infinite electron gas system to study finite systems, the major source of error comes from the fact that the low-lying levels of a finite system are discrete and have finite spacings. The replacement of summation by integration in the perturbation diagrams results in an overestimate of correlation energy, and a small error in the exchange energy in a finite system like an atom.