FERROMAGNETISM IN THE HUBBARD-MODEL ON LINE GRAPHS AND FURTHER CONSIDERATIONS

Let L(G) be the line graph of a graph G = (V, E). The Hubbard model on L(G) has ferromagnetic ground states with a saturated spin if the interaction is repulsive ( U > 0) and if the number of electrons N satisfies N greater-than-or-equal-to M. M = (E) + (V) - 1 if G is bipartite and M = (E) + (V) otherwise. We show that the ferromagnetic ground state is unique if N = M. Further we give a sufficient condition for the existence of other ground states if N > M. The results are valid also for a multi-band Hubbard model on a bipartite graph. In the case of a periodic lattice, the results are related to the existence of a flat energy band.