Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation
Bach, Volker ; Lieb, Elliott H. ; Travaglia, Marcos V.
arXiv, 0506695 / Harvested from arXiv
Text on arXiv
As a contribution to the study of Hartree-Fock theory we prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential mu) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree-Fock theory we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, {S}_z = sum_x n_{x,\uparrow} - n_{x,\downarrow}, and we find that the choice 2{S}_z = N = particle number gives the lowest energy at fixed 0 < mu < 4d.
Publié le : 2005-06-27
Classification:  Condensed Matter - Strongly Correlated Electrons,  Condensed Matter - Statistical Mechanics,  Mathematical Physics 
@article{0506695,
     author = {Bach, Volker and Lieb, Elliott H. and Travaglia, Marcos V.},
     title = {Ferromagnetism of the Hubbard Model at Strong Coupling in the
  Hartree-Fock Approximation},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506695}
}

Bach, Volker; Lieb, Elliott H.; Travaglia, Marcos V. Ferromagnetism of the Hubbard Model at Strong Coupling in the
  Hartree-Fock Approximation. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506695/