Accuracy of the Hartree-Fock approximation for the Hubbard model

A lower bound 0 greater than or equal to(E(gs)(n)-E(hf)(n))/\Lambda\greater than or equal to-const[nu(2/3)U(4/3) (\ln U\ + 1) + Un(1/2)\Lambda\(-1/2d)(\ln(\Lambda\(-1/2))\1)] to the difference of the ground state and the Hartree-Fock energy of the Hubbard model is derived. Here \Lambda\ is the lattice size, U is the coupling parameter, and n is the electron density per site. This estimate holds for all dimensions d greater than or equal to 2 and all densities. Thus the Hartree-Fock approximation becomes exact (even beyond terms of order U) for small U and large \Lambda\. (C) 1997 American Institute of Physics.