Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice I

In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid phase taking place at zero temperature between the quantum liquid and the solid. In this and a succeeding paper, we re-visit this issue for a few polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L * L square lattice with periodic boundary conditions and nearest neighbor hopping.