DMRG simulations of a 3 band Hubbard model for the cuprates

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 a density-matrix-renormalization-group calculation 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 pairfield response has an $d_{x^2-y^2}$-like structure for both the hole and electron doped systems.