Ground State of Two-Dimensional Electrons in Strong Magnetic Fields and $\frac{1}{3}$ Quantized Hall Effect

The authors have diagonalized numerically the Hamiltonian of a two-dimensional system of up to six interacting electrons, in the lowest Landau level, in a rectangular box with "periodic" boundary conditions. They find that the ground state has a pair correlation function quite different from that of a Wigner crystal, and its energy is significantly lower. They also find some indications of a downward cusp in the energy at $\frac{1}{3}$ filling.