Clustering and the ground state of interacting 2D electrons in a magnetic field

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Abstract
Ground-state energies are computed for interacting 2D electrons subject to periodic boundary conditions in a magnetic field. When the aspect ratio of the periodic cell is small the ground-state energy as a function of magnetic field is found to have cusp-like minima when the number of flux quanta is a multiple of the number of electrons. However, the cusps at even-order fractional filling tend to disappear when the aspect ratio of the periodic cell is increased. This effect is explained in terms of a competition between direct and exchange interactions which favours clustered configurations of electrons when the aspect ratio is large.