2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165950The $t-J$ and Heisenberg models are truncated expansions of a canonically transformed Hubbard model coinciding with it at $U\to \infty$. We show that a modified canonical transformation applied to the Hubbard model leads to alternative models of the same form, but whose convergence properties with respect to the expansion are more favourable, resulting in a good description of the half-filled ground state even at $0<U\leq1$. We investigate the transformed Hamiltonian and observables for metallic and insulating variational wave-functions.to appear in Physical Review B (Brief reports) added author names and addresses (which were missing in the first version) revised version: 1. There was an error in Fig. 2, now fixed. 2. Minor text revisionsStrongly Correlated ElectronsSuperconductivitytext