Fermion N-Representability Conditions Generated by a Decomposition of the 1-Particle Identity Operator onto Mutually Orthogonal Projection Operators

Abstract

In reduced density matrix theory [1, 14, 26, 28], a state, ψ^N, is represented by its 2-particle reduced density operator D² (ψ^N). The set, P ²_N , of all fermion reduced 2-density operators is a convex set and the ground state energy of a system can be determined variationally by minimizing the functional $E = \begin{array}{*{20}{l}} {\inf (_2^N)Tr({h^2}{D^2})} \\ {{D^2} \in P_N^2} \end{array}$ over the set P ²_N (h² is the reduced hamiltonian). However, a complete characterization of P ²_N has not yet been given. It has been shown [22] that the knowledge of all exposed points of P ²_N is sufficient to characterize the closure of P ²_N . The dual characterization of P ²_N involves determination of the polar cone $\tilde P_N^2.$.