As a contribution to the study of the 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 μ) 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 = ∑x n x,↑ -nx,↓, and we find that the choice 2S*Z = N = particle number gives the lowest energy at fixed 0 < μ, < 4d.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Hartree-Fock theory
- Hubbard model