Fluctuation-exchange theory for general lattice Hamiltonians

The fluctuation-exchange, or FLEX, approximation for interacting electrons is derived for lattice Hamiltonians with general instantaneous one- and two-body terms. The use of a two-body basis set indexed by relative separation, rather than relative momentum, is emphasized. The fluctuation-exchange approximation for the three-orbital ${\mathrm{CuO}}_2$ model with on-site and near-neighbor Coulomb interactions is solved for one-particle properties. Unit-cell densities corresponding to both ``hole doping'' and ``electron doping'' are studied. The model is found to be far from a charge-density instability for all reasonable parameter values. The only nearly unstable particle-hole channel for unit-cell densities close to unity has Q∼(π,π) and S=1 (antiferromagnetic). The Fermi surface of the interacting system is computed, and the Luttinger theorem verified numerically in its most general context. Orbital-projected occupancy factors and spectral densities are examined.