Variational Principle for Many-Fermion Systems

  • Elliott H. Lieb


If ψ is a determittantal variational trial function for the N-fermion Hamiltonian, H with one- and two-body terms, then e 0 ≤ 〈ψ,Hψ〉 = E(K) where e 0 is the ground-state energy, K is the one-body reduced density matrix of ψ, and E(K) is the well-known expression in terms of direct and exchange energies. If an arbitrary one-body K is given, which does not come from a determinantal ψ then E(K) ≥e 0 does not necessarily hold. It is shown, however, that if the two-body part of H is positive, then in fact e 0e HFE(K) where e HF is the Hartree-Fock ground-state energy.


Variational Principle Positive Semidefinite Pauli Principle Diagonal Case Itinerant Ferromagnetism 
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  1. ’A. Horn, Am. J. Math. 76, 620 (1954).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  1. 1.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA

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