Band theory of magnetism in metals in context of exactly soluble model

Abstract

The role of spatial forces, and of Hund’s rule (exchange) forces, and the validity of the Hartree-Fock approximation in the band theory of magnetism of metals is reviewed. Some reasonable conjectures which have been made elsewhere by the author and others are examined in the light of an exactly soluble model of interacting electrons in one dimension. It is shown that within the framework of validity of this model, spatial i.e., direct (Coulomb) forces do not influence the spin susceptibility, and conversely, Hund’s rule exchange forces do not affect the dielectric constant or plasmon spectrum. It is recalled that the time-independent Hartree-Fock approximation yields an incorrect spectrum of elementary excitations, and it is also shown explicitly that the magnetic susceptibility calculated in this approximation is incorrect. A paradox is noted, concerning whether “correlations” can in fact correct the errors in the H-F approximation. Finally, it is shown that when there are only space forces, such spin density waves as might be introduced in to the H-F ground state of the model are in fact spurious, because they are not representative of the correlations which exist in the true ground state.