Fermionic natural occupation numbers (NON) do not only obey Pauli's famous exclusion principle, but are even further restricted to a polytope by the generalized Pauli constraints, conditions which follow from the fermionic exchange statistics. Whenever given NON are pinned to the polytope's boundary, the corresponding $N$-fermion quantum state $|{\Psi }_N\rangle$ simplifies due to a selection rule. We show analytically and numerically for the most relevant cases that this rule is stable for NON close to the boundary, if the NON are nondegenerate. In case of degeneracy, a modified selection rule is conjectured and its validity is supported. As a consequence, the recently found effect of quasipinning is physically relevant in the sense that its occurrence allows to approximately reconstruct $|{\Psi }_N\rangle$, its entanglement properties, and correlations from one-particle information. Our finding also provides the basis for a generalized Hartree-Fock method by a variational ansatz determined by the selection rule.

• Received 9 July 2014

DOI:https://doi.org/10.1103/PhysRevA.91.022105