Long-range Coulomb repulsion and finite-size approximations

We show that when sizable long-range Coulomb repulsion is included in numerical studies of small clusters, different sizes and shapes should be considered to obtain a ground state which represents correctly the physics of the ground state (GS) in the thermodynamic limit. Also cutting off the interaction at small distances might lead to a spurious GS. In particular the GS reported in the literature for the two-dimensional three-band Hubbard model in the static limit at hole concentratoin x=0.25 is in fact a slightly excited state when an important (screened or not) Coulomb repulsion at all distances is included