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Ground state of the half-filled extended Hubbard model beyond the Hartree-Fock approximation

Andrzej M. Oleś, R. Micnas, S. Robaszkiewicz +1 more

Physics Letters AMay 1, 198413 citations

The Ground State Energy of the Hubbard Model in Hubbard's Approximation

Rainer J. Jelitto

Abstract We have calculated the ground state energy of the Hubbard model in the approximation of Hubbard's first paper1 . For the neutral model with nearest neighbour interaction the energy resulting from the selfconsistent paramagnetic solution is compared with those ones following from the (ferromagnetic) Hartree-Fock and an (antiferromagnetic) single particle theory. The energy of the latter one turns out to be the best approximation of the true ground state energy of the model for all values of the coupling constant V0 , but the energy derived from Hubbard's approximation, in spite of the absence of magnetic ordering, is a reasonable approximation at least for sufficiently large values of V0.Abstract We have calculated the ground state energy of the Hubbard model in the approximation of Hubbard's first paper1 . For the neutral model with nearest neighbour interaction the energy resulting from the selfconsistent paramagnetic solution is compared with those ones following from the (ferromagnetic) Hartree-Fock and an (antiferromagnetic) single particle theory. The energy of the latter one turns out to be the best approximation of the true ground state energy of the model for all values of the coupling constant V0 , but the energy derived from Hubbard's approximation, in spite of the absence of magnetic ordering, is a reasonable approximation at least for sufficiently large values of V0.

Zeitschrift für Naturforschung AJun 1, 19721 citation

Generalized Hartree-Fock theory and the Hubbard model

Volker Bach, Élliott H. Lieb, Jan Philip Solovej

arXiv:cond-mat/9312044Journal of Statistical PhysicsJul 1, 1994222 citations

Ground state energy of Hubbard model

W. D. Langer, Daniel Charles Mattis

Physics Letters AAug 1, 197129 citations

FERROMAGNETISM OF THE HUBBARD MODEL AT STRONG COUPLING IN THE HARTREE–FOCK APPROXIMATION

VOLKER BACH, Élliott H. Lieb, MARCOS V. TRAVAGLIA

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, 𝕊z = ∑x nx,↑ - nx,↓, and we find that the choice 2𝕊z = N = particle number gives the lowest energy at fixed 0 < μ < 4d.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, 𝕊z = ∑x nx,↑ - nx,↓, and we find that the choice 2𝕊z = N = particle number gives the lowest energy at fixed 0 < μ < 4d.

arXiv:cond-mat/0506695Reviews in Mathematical PhysicsJun 1, 200612 citations

Accuracy of the Hartree–Fock approximation for the Hubbard model

Volker Bach, Jurij Poelchau

A lower bound 0⩾(Egs(n)−Ehf(n))/|Λ|⩾−const[n2/3U4/3(|ln U|+1) +Un1/2|Λ|−1/2d(|ln(|Λ|−1/2)|1)] to the difference of the ground state and the Hartree–Fock energy of the Hubbard model is derived. Here |Λ| is the lattice size, U is the coupling parameter, and n is the electron density per site. This estimate holds for all dimensions d⩾2 and all densities. Thus the Hartree–Fock approximation becomes exact (even beyond terms of order U) for small U and large |Λ|.

Journal of Mathematical PhysicsApr 1, 199711 citations

Ground state energies of the hubbard models and the hartree–fock approximation

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