Canonical transformation of the Hubbard model and W=0 pairing: Comparison with exact diagonalization results

We have recently developed a canonical transformation of the Hubbard and re lated models, valid for systems of arbitrary size and for the full plane; t his is particularly suited to study hole pairing. In this work we show that exact diagonalization results of the one band Hubbard model for small clus ters with periodic boundary conditions agree well with the analytical ones obtained by means of our canonical transformation. In the presence of a pai ring instability, the analytic approach allows us to identify the Cooper pa irs. They are W=0 pairs, that is. singlet two-hole eigenstates of the Hubba rd Hamiltonian with vanishing on-site repulsion. Indeed, we find that the C oulomb interaction effects on W=0 pairs are dynamically small, and repulsiv e or attractive, depending on the filling.