Two Theorems on the Hubbard Model

In the attractive Hubbard model (and some extended versions of it), the ground state is proved to have spin angular momentum S = 0 for every (even) electron filling. In the repulsive case, and with a bipartite lattice and a half-filled band, the ground state has S = 1/2 || B |—| A ||, where |B| ( |A| ) is the number of sites in the B (A) sublattice. In both cases the ground state is unique. The second theorem confirms an old, unproved conjecture in the |B| = |A| case and yields, with | B | ≠ | A|, the first provable example of itinerant-electron ferromagnetism. The theorems hold in all dimensions without even the necessity of a periodic lattice structure.