Abstract
Numerical diagonalization of the Hamiltonian is done for a two dimensional system of up to six interacting electrons, in the lowest Landau level, in a rectangular box with periodic boundary conditions. It is found that the ground state is not a Wigner crystal but a liquid-like state. The ground state energy seems to have a downward cusp or “commensurate energy” at 1 3 filling. Although the nature of the ground state is still not clear, the magnitude of the cusp is consistent with the experimentally observed anomaly in σ xy and σ xx at 1 3 filling by Tsui, Störmer and Gossard (Phys. Rev. Letters 48 (1982) 1559). Several properties of the ground state are also investigated.
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