GENERALIZED HARTREE-FOCK THEORY AND THE HUBBARD-MODEL

The familiar unrestricted Hartree-Fock variational principle is genera lized to include quasi-free states. As we show, these are in one-to-on e correspondence with the one-particle density matrices and these. in turn, provide a convenient formulation of a generalized Hartree-Fock v ariational principle, which includes the BCS theory as a special case. While this generalization is not new, it is not well known and we beg in by elucidating it. The Hubbard. model, with its particle hole symme try, is well suited to exploring this theory because BCS states for th e attractive model turn into usual HF states for the repulsive model. We rigorously determine the true, unrestricted minimizers for zero and for non-zero temperature in several cases, notably the half-fitted ba nd. For the cases treated here. we can exactly determine all broken an d unbroken spatial and gauge symmetries of the Hamiltonian.