Doping Asymmetry of a 3-orbital CuO$_2$ Hubbard Model

While both the hole and electron doped cuprates can exhibit $d_{x^2-y^2}$-wave superconductivity, the local distribution of the doped carriers is known to be significantly different with the doped holes going primarily on the O sites while the doped electrons go on the Cu sites. Here we report the results of density matrix renormalization calculations for a three-orbital model of a CuO$_2$ lattice. In addition to the asymmetric dependence of the intra-unit-cell occupation of the Cu and O for hole and electron doping, we find important differences in the longer range spin and charge correlations. As expected, the pair-field response has a $d_{x^2-y^2}$-like structure for both the hole and electron doped systems.