1993/12/10 by Volker Bach, Elliott H. Lieb, Jan Philip Solovej +1 · 11 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #cond-mat
paper · pdf · doi:10.1007/bf02188656
68 pages Plain TeX, VBEHLJPS-25/nov/93
arxiv created 1993/12/10 · openalex publication_date 1994/07/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.