Abstract
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∣ (resp. ∣A∣) is the number of sites in the B (resp. A) sublattice. In both cases the ground state is unique. These theorems hold for all values of U, the attraction or repulsion parameter. The second theorem confirms an old, unproved conjecture in the ∣B∣ = ∣A∣ case; the generalization given here yields, with ∣B∣ ≠ ∣A∣, the first provable example of itinerant electron ferromagnetism. Since topology is irrelevant for the proofs, the theorems hold in all dimensions without even the necessity of a periodic lattice structure.
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