Finite-cluster studies of the fractional filling of the Landau level

Abstract
Finite-cluster systems of a two-dimensional electron gas under a high magnetic field are investigated by numerical diagonalisation of the Hamiltonians. A detailed study is presented of the system of three Coulomb interacting electrons in particular. The contribution from the uniform neutralising background is included. The numerical result for the ground-state energy at a filling factor of 1/3 is in good agreement with that for the incompressible fluid.