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Hartree Fock and RPA Studies of the Hubbard Model

F. Guinea, Enrique Louis, José Antonio Vergés

NATO ASI series. Series B : PhysicsJan 1, 19950 citations

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

Jacek Wojtkiewicz, Piotr H. Chankowski

arXiv:2209.02361Reports on Mathematical PhysicsOct 1, 20231 citation

Generalized Hartree-Fock Theory And The Hubbard Model

Volker Bach, Élliott H. Lieb, Jan Philip Solovej

: The familiar unrestricted Hartree-Fock variational principle is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matrices and these, in turn provide a convenient formulation of a generalized Hartree-Fock variational principle, which includes the BCS theory as a special case. While this generalization is not new, it is not well known and we begin by elucidating it. The Hubbard model, with its particle-hole symmetry, is well suited to exploring this theory because BCS states for the attractive model turn into usual HF states for the repulsive model. We rigorously determine the true, unrestricted minimizers for zero and for nonzero temperature in several cases, notably the half-filled band. For the cases treated here, we can exactly determine all broken and unbroken spatial and gauge symmetries of the Hamiltonian. This work was supported in part by Sonderforschungsbereich 288 of the Deutsche Forschungsgemeinschaft...: The familiar unrestricted Hartree-Fock variational principle is generalized to include quasi-free states. As we show, these are in one-to-one correspondence with the one-particle density matrices and these, in turn provide a convenient formulation of a generalized Hartree-Fock variational principle, which includes the BCS theory as a special case. While this generalization is not new, it is not well known and we begin by elucidating it. The Hubbard model, with its particle-hole symmetry, is well suited to exploring this theory because BCS states for the attractive model turn into usual HF states for the repulsive model. We rigorously determine the true, unrestricted minimizers for zero and for nonzero temperature in several cases, notably the half-filled band. For the cases treated here, we can exactly determine all broken and unbroken spatial and gauge symmetries of the Hamiltonian. This work was supported in part by Sonderforschungsbereich 288 of the Deutsche Forschungsgemeinschaft...

Jan 1, 1994144 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

Random-phase approximation for multi-band Hubbard models

Jörg Bünemann, Florian Gebhard

We derive the random-phase approximation for spin excitations in general multi-band Hubbard models, starting from a collinear ferromagnetic Hartree-Fock ground state. The results are compared with those from a recently introduced variational many-body approach to spin waves in itinerant ferromagnets. As we exemplify for Hubbard models with one and two bands, the two approaches lead to qualitatively different results. The discrepancies can be traced back to the fact that the Hartree-Fock theory fails to describe properly the local moments which naturally arise in a correlated-electron theory.We derive the random-phase approximation for spin excitations in general multi-band Hubbard models, starting from a collinear ferromagnetic Hartree-Fock ground state. The results are compared with those from a recently introduced variational many-body approach to spin waves in itinerant ferromagnets. As we exemplify for Hubbard models with one and two bands, the two approaches lead to qualitatively different results. The discrepancies can be traced back to the fact that the Hartree-Fock theory fails to describe properly the local moments which naturally arise in a correlated-electron theory.

arXiv:cond-mat/0107050Journal of Physics Condensed MatterOct 19, 20015 citations

Fermionization and Hubbard models

P. Dargis, Z. Maassarani

arXiv:cond-mat/9806208Nuclear Physics BDec 1, 199810 citations

Generalized Hartree-Fock theory and the Hubbard model

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