Self-Consistent Pair Correlations in Mott-Type Insulators

A simple cubic hydrogenic lattice with the Hubbard Hamiltonian is used as a model for Mott-type insulators. A new self-consistent approximation is developed by the decoupling of four-particle Green's functions, leading to a higher-order Hartree-like eigenvalue equation for electron-hole Green's functions. This equation is an improvement over the previously used Ω approximation. The solution of the eigenvalue equation leads to the conjecture that an exact solution (i.e., one without decoupling) would result in each atom having exactly one electron.