COMBINATORIAL APPROACH TO N-REPRESENTABILITY OF P-DENSITY MATRICES

This paper considers the determination of N-representability (for diagonal elements) of p-density matrices restricted to certain finite-dimensional subspaces of l2 of the configuration space of N identical antisymmetric particles. In particular, an arbitrary set of N + p spin orbitals is selected and one considers the (Np+p-dimensional subspace generated by all possible Slater determinants of the spin orbitals being considered. Applying a combinatorial approach to the problem, a necessary and sufficient set of conditions is determined; previous work has dealt only with necessary conditions, except in the 1-matrix case. The paper concludes by presenting a probabilistic interpretation of these conditions which seems of particular interest for the 2-matrix case. The conditions presented here in combination with the Pauli principle give a probabilistic view of the expected occupation of p-tuples of spin orbitals in terms of the expected occupations of lower-order-tuples of spin orbitals.