Cluster diagonalization in systematically expanded Hilbert spaces: Application to models of correlated electrons

A method of cluster diagonalization in a systematically expanded Hilbert space is described. We discuss some applications of this procedure to models of high-${\mathit{T}}_{\mathit{c}}$ superconductors, like the t-J model and the one- and three-band Hubbard models in two dimensions. The results obtained with this method are compared against results obtained with other techniques dealing with truncated Hilbert spaces. The relation between this method of diagonalization in a reduced Hilbert space, and perturbation theory and variational techniques is also discused.