Variational Principle for Many-Fermion Systems

Abstract

If ψ is a determinantal variational trial function for the N-fermion Hamiltonian, H, with one- and two-body terms, then e₀≤〈ψ, Hψ〉=E(K), where e₀ 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)≥e₀ does not necessarily hold. It is shown, however, that if the two-body part of H is positive, then in fact e₀≤e_HF≤E(K), where e_HF is the Hartree-Fock ground-state energy.