Phase diagrams of the electronic state of the one-dimensionald-pmodel

We investigate the one-dimensional (1D) d-p model, simulating a Cu-O linear chain with strong Coulomb repulsion, by using the numerical diagonalization method. Using the Luttinger liquid theory, we obtained phase diagrams of the ground state on ${\mathit{U}}_{\mathit{d}}$-${\mathit{U}}_{\mathit{p}\mathit{d}}$ plane, where ${\mathit{U}}_{\mathit{d}}$ and ${\mathit{U}}_{\mathit{p}\mathit{d}}$ represent on-site interaction at d sites and the nearest-neighbor interaction between p and d sites, respectively. In the weak-coupling region, they agree with the g-ology; a superconducting phase [SC(I)] is restricted to attractive interaction ${\mathit{U}}_{\mathit{p}\mathit{d}}$‖${\mathit{U}}_{\mathit{d}}$‖ and an insulating state with a charge gap for ${\mathit{U}}_{\mathit{d}}$>${\mathit{U}}_{\mathit{d}}^{\mathit{c}}$ and ${\mathit{U}}_{\mathit{p}\mathit{d}}$>${\mathit{U}}_{\mathit{p}\mathit{d}}^{\mathit{c}}$ with critical values ${\mathit{U}}_{\mathit{d}}^{\mathit{c}}$ and ${\mathit{U}}_{\mathit{p}\mathit{d}}^{\mathit{c}}$ at half-filling. Away from half-filling, another superconducting phase [SC(III)] appears for ${\mathit{U}}_{\mathit{d}}$≫${\mathit{U}}_{\mathit{p}\mathit{d}}$>0; which has been found for ${\mathit{U}}_{\mathit{d}}$→∞ in the previous paper [Physica C 205, 170 (1993)]. An analysis of the spin gap suggests that the SC(I) and SC(II) include the Luther-Emery region (with spin gap) in part, while the SC(III) belongs to the Tomonaga-Luttinger region (without spin gap) in whole.