Interaction effects near constriction of a quasi two-dimensional electron system: an exact diagonalization study

We present a systematic exact diagonalization study of a quasi two-dimensional few-electron system in a closed three-dimensional cylindrical geometry containing a constriction that models a quantum point contact formed within the two-dimensional electron gas. The calculations that are performed using the configuration interaction approach with multicenter Gaussian basis indicate that the tendency of the majority spin to gather in the area of an increased effective potential - e.g. by constriction of the quantum point contact - is distinct already for weak constrictions and low electron numbers. Opposite effects - nearly equal spin up and spin down densities - are obtained for local cavities of the confinement potential. Formation of a quasi-bound single-spin island within the constriction is also discussed.