Coupled-spin-mobile-hole model for high-Tcsuperconducting oxides

A model representing a system of coupled localized spins and mobile holes and relevant to superconducting oxides is analyzed by performing both exact diagonalizations on small systems and variational calculations. Ground-state expectation values, susceptibilities, optical conductivity, and pairing correlations are calculated for systems with up to six unit cells arranged on a ring or representing a square lattice. With increasing spin-mobile-hole coupling, our results show a transition to a regime of mobile singlets and short-range magnetic correlations. On the square lattice, the interaction weakly enhances the $d$-wave pairing, but suppresses $s$-wave and extended $s^{*}$-wave correlations.