Two theorems on the Hubbard model

Elliott H. Lieb

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1733 Scopus citations


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- -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.

Original languageEnglish (US)
Pages (from-to)1201-1204
Number of pages4
JournalPhysical review letters
Issue number10
StatePublished - 1989

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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