QUANTUM CORRECTIONS TO THE WIGNER CRYSTAL - A HARTREE-FOCK EXPANSION

The quantum corrections to the two-dimensional Wigner crystal, for fil ling nu less-than-or-equal-to 1/3, are discussed by using a Hartree-Fo ck expansion based on wave functions which are (i) related to one anot her by magnetic translations, (ii) orthonormal, and (iii) strongly loc alized. Such wave functions are constructed in terms of Gaussians that are localized at the sites of a triangular (Wigner) lattice and have a small overlap c. The ground-state energy per particle is calculated by an expansion in square-root nu and in delta=c1/4, which is rapidly convergent and stable under the thermodynamical limit. In particular, in this limit the cancellation of the infrared divergences occur order by order in the above expansion. The accurate control on the approxim ations allows a clear-cut comparison with the energy obtained by the L aughlin ansatz on the ground state and the numerical results confirm t hat the Wigner-crystal picture is energetically favored with respect t o the Laughlin state for nu < 1/9.