Doping-induced metal-insulator transition in two-dimensional Hubbardt−Uand extended Hubbardt−U−Wmodels

We show numerically that the nature of the doping-induced metal-insulator transition in the two-dimensional Hubbard model with hopping matrix element $t$ and Coulomb repulsion $U$ is radically altered by the inclusion of a term $W$ that 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 $W/t=0.05\mathrm{}$ and $U/t=4\mathrm{}$, 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 $U/t=4\mathrm{}$. At half-filling, we calculate the density of states $N\left(\omega \right)$. The large value of $N\left(\omega \right)$ in the vicinity of $\omega ={\mu }_c$ present at $W=0\mathrm{}$ is suppressed with growing values of $W$. At finite doping, the $d$-wave pair-field correlations are enhanced with growing values of $W$. The numerical results imply that at finite values of $W$ doping the antiferromagnetic Mott insulator leads to a $d_{x^2-y^2}$ superconductor.