Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 195

Accuracy of the Hartree-Fock Approximation for the Hubbard Model

V. Bach, J. Poelchau

A lower bound $0 geq igl( E_{gs}(n) - E_{hf}(n) igr)/LBgeq - const igl[ n^{2/3} , U^{4/3}(|ln U| + 1) , + , U n^{1/2} LB ^{-1/2d} (|ln (LB^{-1/2})| + 1 ) igr] $ to the difference of the ground state- and the Hartree-Fock energy of the Hubbard model is derived. $LB$ is the lattice size, $U$ is the coupling parameter, and $n$ is the electron density per site. This estimate holds for all dimensions $d geq 2$ and all densities. Thus the Hartree-Fock approximation becomes exact (even beyond terms of order $U$) for small $U$ and large $LB$.

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