  We show numerically that the nature of the doping induced metal-insulator
transition in the two-dimensional Hubbard model is radically altered by the
inclusion of a term, $W$, which depends upon a square of a single-particle
nearest-neighbor hopping. This result is reached by computing the localization
length, $\xi_l$, in the insulating state. At finite values of $W$ we find
results consistent with $\xi_l \sim | \mu - \mu_c|^{- 1/2} $ where $\mu_c$ is
the critical chemical potential. In contrast, $\xi_l \sim | \mu -
\mu_c|^{-1/4}$ for the Hubbard model. At finite values of $W$, the presented
numerical results imply that doping the antiferromagnetic Mott insulator leads
to a $d_{x^2 - y ^2}$ superconductor.
