ELECTRON CORRELATION IN NARROW ENERGY BANDS .2. ONE REVERSED SPIN IN AN OTHERWISE FULLY ALIGNED NARROW S BAND

In a previous paper, a new Green's-function decoupling scheme was applied to the Hubbard Hamiltonian, and an improved version of Hubbard's first approximation was obtained. That result did not reduce to the correct low-density limit as obtained by Kanamori. In the present article, the theory is improved for the special case of a single reversed spin in an otherwise fully aligned band, and the improved theory is correct in the low-density limit. Numerical results are presented for the simple cubic lattice. If we define an effective exchange-interaction parameter Ueff as the k=0 reversed-spin self-energy for U→, divided by the number na of up-spin electrons per site, we find that the present result departs rather rapidly from the Kanamori result as na is increased, and it is concluded that the Kanamori result overestimates the increase in Ueff with na, at least in the present case. For intermediate values of na, the two-pole approximation of the previous article and the present calculation give very similar results for this quantity. © 1969 The American Physical Society.