Two theorems on the Hubbard model
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|| (||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.
- Publication:
-
Physical Review Letters
- Pub Date:
- March 1989
- DOI:
- 10.1103/PhysRevLett.62.1201
- Bibcode:
- 1989PhRvL..62.1201L
- Keywords:
-
- 75.10.Lp;
- 71.20.Ad;
- 74.65.+n;
- Band and itinerant models