Ferromagnetism in the Hubbard model and Hund's rule

Abstract

We investigate the Hubbard model with a N d-fold degenerate single particle ground state. If the number of electrons satisfies N e⩽ N d, the model has ferromagnetic multiparticle ground states. We give a necessary and sufficient condition for the ground state to be unique if N e= N d. It is ferromagnetic with a spin S= 1 2 N e . As a corollary, we obtain Hund's rule for the general Hubbard model with degenerate single particle eigenstates on translationally invariant lattices in the special case, where each of the degenerate single particle states is filled with one electron.