4 M ay 1 99 6 Ferromagnetism in the Hubbard model with an infinite - range hopping

Ferromagnetism in the Hubbard model with an infinite-range hopping. Abstract We prove, as recently conjectured, that the ground state of the Hub-bard Hamiltonian with an infinite-range hopping, when the number of electrons N e = N + 1 (N being the number of sites), is ferromagnetic fully polarized. Despite its long history, the problem of itinerant ferromagnetism is still, to many regards, an open question. The Hubbard model was considered from the beginning as a good model to investigate this intriguing problem [1]. However, rigorous examples of ferromagnetism in the Hubbard model have been shown only in some rather peculiar situations: Nagaoka ferromagnetism for infinite Hubbard repulsion U and one hole in a half-filled band [2] (see [3] for a very elegant proof of Nagaoka's theorem), Lieb ferrimagnetism for half-filled bipartite lattices with sublattices containing a different number of sites [4] and the flat (or nearly-flat) band of Mielke [5] and Tasaki [6]. Besides these rigorous results, some recent numerical and analytical investigations seem to indicate the existence of a fully polarized ferromagnetic ground state in the one dimensional Hubbard model with nearest and next-nearest-neighbour hopping [7, 8]. In the presence of so few results, it is clear that every new example of ferromagnetism in a Hubbard model is of great interest. Very recently some conjectures about the ground state of the Hubbard model 1