Phase diagrams of the electronic state of the one-dimensional [ital d]-[ital p] model

We investigate the one-dimensional (1D) [ital d]-[ital 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 [ital U][sub [ital d]][minus][ital U][sub [ital p][ital d]] plane, where [ital U][sub [ital d]] and [ital U][sub [ital p][ital d]] represent on-site interaction at [ital d] sites and the nearest-neighbor interaction between [ital p] and [ital d] sites, respectively. In the weak-coupling region, they agree with the [ital g]-ology; a superconducting phase [SC(I)] is restricted to attractive interaction [ital U][sub [ital p][ital d]][lt]0. On the other hand, in the strong-coupling region, we found a superconducting phase [SC(II)] for repulsive interaction [ital U][sub [ital p][ital d]][gt][vert bar][ital U][sub [ital d]][vert bar] and an insulating state with a charge gap for [ital U][sub [ital d]][gt][ital U][sub [ital d]][sup [ital c]] and [ital U][sub [ital p][ital d]][gt][ital U][sub [ital p][ital d]][sup [ital c]] with critical values [ital U][sub [ital d]][sup [ital c]] and [ital U][sub [ital p][ital d]][sup [ital c]] at half-filling. Away from half-filling, another superconducting phase [SC(III)] appears for [ital U][sub [ital d]][much gt][ital U][sub [ital p][ital d]][gt]0; which has been found formore » [ital U][sub [ital d]][r arrow][infinity] 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.« less