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Variational Principle for Many-Fermion Systems

  • Elliott H. Lieb

Abstract

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.

Keywords

Variational Principle Positive Semidefinite Pauli Principle Diagonal Case Itinerant Ferromagnetism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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