Ferromagnetism in correlated electron systems: Generalization of Nagaoka's theorem

Nagaoka's theorem on ferromagnetism in the Hubbard model with one electron fewer than half filling is generalized to the case where all possible nearest-neighbor Coulomb interactions (the density-density interaction V, bond-charge interaction X, exchange interaction F, and hopping of double occupancies F^') are included. It is shown that for ferromagnetic exchange coupling ($F>0$) ground states with maximum spin are stable already at finite Hubbard interaction U>Uc. For nonbipartite lattices this requires a hopping amplitude $t<~0$. For vanishing F one obtains Uc→∞ as in Nagaoka's theorem. This shows that the exchange interaction F is important for stabilizing ferromagnetism at finite U. Only in the special case $X=t$ is the ferromagnetic state stable even for $F=0$, provided the lattice allows the hole to move around loops.