Ground state energy of two dimensional electrons in strong magnetic fields: Small clusters in fractional occupations

Abstract

We diagonalize numerically the Hamiltonian for a two-dimensional system of up to seven interacting via Coulomb force electrons in a strong magnetic field using the symmetric gauge. The effect of positive charge background is taken into account. We find significant downward cusps for certain values of the total angular momentum corresponding to fractional occupation of the lowest Landau level in agreement with results obtained by using Landau gauge. This commensurate energy for fractional occupation is interpreted in terms of the “closest configuration” in the space of single particle angular momentum.