Band Ferromagnetism versus Collective Kondo State in Lattice Fermion Models*

It is becoming widely recognized that, contrary to earlier expectations, the usual one-band Hubbard model does not give an explanation for itinerant ferromagnetism. After reviewing the status of magnetic ordering in the one-band model, we discuss the possibility of ferromagnetism in some recently introduced two-band Hubbard models, and in generalized Ander-son lattices. It is argued that these two classes of models are closely related and that it is their common feature that the ferromagnetic phase has to compete with a collective Kondo state. Over three decades of intense research effort have been spent on mapping out the phase diagram of the single-orbital Hubbard model (Hubbard 1963) H = −t i,j σ (c † iσ c jσ + H.c.) + U n i↑ n i↓. It has been usual to treat the case when the summation over i, j extends over the sites of a Bravais lattice (typically, the d-dimensional cubic lattice); then a single atomic orbital gives rise to a single tight binding band. In such cases, the expressions " single-orbital " , and " single-band " can be used synonymously. Recent work on carefully constructed non-Bravais lattices made us aware of the potential importance of single-orbital multi-band Hubbard models. Degenerate or multi-orbital Hubbard models and their extended versions are introduced by a completely different physical motivation, but they can be made formally equivalent to single-orbital models with a larger number of sites per unit cell.