Parametrized canonical transformation for the Hubbard-model at arbitrary interaction strength

The $t-J$ 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.