Phase diagrams of electronic state on One Dimensional d-p Model

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 $U_d-U_{pd}$ plane, where $U_d$ and $U_{pd}$ 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 $U_{pd}|U_d|$ and a insulating state with a charge gap for $U_d>U_d^c$ and $U_{pd}>U_{pd}^c$ with critical values $U_d^c$ and $U_{pd}^c$ at half-filling. Away from half-filling, another superconducting phase (SC(III)) appears for $U_d>>U_{pd}>0$; which has been found for $U_d\to \infty$ in the previous paper [Physica {\bf C205} (1993) 170]. 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 Tomonaga-Luttinger region (without spin-gap) in whole.