Spectra, Moments, and Lattice Walks for Hubbard Magnetic Insulators

Abstract

Density of states and exciton-line-shape spectra in the atomic limit of Mott-Hubbard models are calculated for various distributions of spins: ferromagnetic, antiferromagnetic, antiferromagnetic in planar layers, are random or paramagnetic. The spectra are obtained by extrapolating and fitting the leading six to twelve moments. These moments can be obtained by enumerating certain "random" walks on the space lattice. Particular emphasis is given to the mathematical aspects of the problem. With the aid of generating-function techniques, exact solutions are obtained for the ferromagnetic distribution and for certain classes of auxiliary walks which lead to accurate approximations for other spin configurations. The necessary additional counting and weighting methods are developed to yield exact leading moments for the simple cubic lattice.