Mean-field results of the multiple-band extended Hubbard model for the square-planar ${\mathrm{CuO}}_2$ lattice

We obtain metal-insulator phase diagrams at half-filling for the five-band extended Hubbard model of the square-planar ${\mathrm{CuO}}_2$ lattice treated within a Hartree-Fock mean-field approximation, allowing for spiral spin-density waves. We indicate the existence of an insulating phase (covalent insulator) characterized by strong covalency effects, not identified in the earlier Zaanen-Sawatzky-Allen phase diagram. While the insulating phase is always antiferromagnetic, we also obtain an antiferromagnetic metallic phase for a certain range of interaction parameters. Performing a nonperturbative calculation of ${\mathit{J}}_{\mathrm{eff}}$, the in-plane antiferromagnetic interaction is presented as a function of the parameters in the model. We also calculate the band gap and magnetic moments at various sites and discuss critically the contrasting interpretation of the electronic structure of high-${\mathit{T}}_{\mathit{c}}$ materials arising from photoemission and neutron-scattering experiments.