Generalized Hartree-Fock theory and the Hubbard model

Volker Bach, Elliott H. Lieb, Jan Philip Solovej

Research output: Contribution to journalArticlepeer-review

135 Scopus citations

Abstract

The familiar unrestricted Hartree-Fock variational principles 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.

Original languageEnglish (US)
Pages (from-to)3-89
Number of pages87
JournalJournal of Statistical Physics
Volume76
Issue number1-2
DOIs
StatePublished - Jul 1994

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Hartree-Fock theory
  • Hubbard model
  • antiferromagnetism
  • symmetry breaking

Fingerprint Dive into the research topics of 'Generalized Hartree-Fock theory and the Hubbard model'. Together they form a unique fingerprint.

Cite this