 93334 Bach V. , Lieb E. H. , Solovej J. P.
 Generalized HartreeFock Theory and the Hubbard Model
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Dec 20, 93

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Abstract. The familiar unrestricted HartreeFock variational principle is
generalized to include quasifree states. As we show, these are in
onetoone correspondence with the oneparticle density matrices and
these, in turn provide a convenient formulation of a generalized
HartreeFock 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
particlehole 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 halffilled band. For the cases treated here, we can
exactly determine all broken and unbroken spatial and gauge symmetries
of the Hamiltonian.
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