Electron Correlation in Narrow Energy Bands. I. The Two-Pole Approximation in a NarrowSBand

Abstract

An improved version of Hubbard's treatment of correlation in a nondegenerate narrow band is obtained by the use of a new Green's-function decoupling scheme. The resulting one-electron Green's function has two poles on the real axis corresponding to a splitting of the electron bands due to the strong correlations between electrons on the same site. This is the same result that Hubbard obtained, but in our case the poles are shifted and their positions agree with the results of Harris and Lange, who used a moment technique. The theory is applied to a simple cubic lattice with nearest-neighbor interaction, and the lattice is found to be ferromagnetic in the strongly correlated limit for a sufficiently large number of electrons per atom. An examination of the low-density limit shows that the two-pole approximation does not reduce to Kanamori's $T$-matrix result, a failing which it shares with Hubbard's theory. A method is outlined for improving the theory so as to give the correct low-density result. In addition, the possibility of obtaining a minimum principle for the theory is explored.