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=½ | | 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.
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References
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© 2004 Springer-Verlag Berlin Heidelberg
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Lieb, E.H. (2004). Two Theorems on the Hubbard Model. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Condensed Matter Physics and Exactly Soluble Models. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06390-3_3
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DOI: https://doi.org/10.1007/978-3-662-06390-3_3
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