Generalized Hartree-Fock theory and the Hubbard model

Journal Article · Fri Jul 01 04:00:00 EDT 1994 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF02188656· OSTI ID:471832

Bach, V ^[1]; Lieb, E H; Solovej, J P ^[2]

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1. Technische Universitaet Berlin (Germany)
2. Princeton Univ., NJ (United States)

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 non-zero 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.

• Sponsoring Organization: USDOE
• OSTI ID: 471832
• Journal Information: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 1-2 Vol. 76; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANTIFERROMAGNETISM
BCS THEORY
HARTREE-FOCK METHOD
HUBBARD MODEL
PARTICLE-HOLE MODEL
SUPERCONDUCTIVITY
SYMMETRY BREAKING