Single-Particle Excitations in Narrow Energy Bands

Hubbard's model for studying correlation effects in systems with narrow energy bands is analyzed by means of a technique which allows the calculation of moments of the individual peaks in the spectral weight function for single-particle excitations. The analysis of the zeroth moments of the peaks shows that the total weight in the bands depends on the strength of the kinetic-energy term in the Hamiltonian even though the bands may be narrow and widely separated. This conclusion is illustrated and verified by an exact calculation for the case when there are only two lattice sites. Analysis of first and higher moments yields results for nonmagnetic or paramagnetic phases which are in qualitative agreement with Hubbard's improved solution. However, we find that (a) there occurs a spin-dependent shift in the band energies which has not been obtained by other treatments of the model and which energetically favors ferromagnetism, and (b) single-particle excitations are more heavily damped in antiferromagnetic than in isomorphic paramagnetic phases.