Selection rules for pinned and quasipinned occupation numbers with degeneracy

Abstract

When the natural occupation numbers of a fermionic state saturate a generalized Pauli constraint, the state obeys a selection rule: only those configurations of natural orbitals that saturate the constraint themselves contribute. Pinning thus singles out an active space. The selection rule was proved for non-degenerate occupation numbers; for degenerate ones it was conjectured, and proved for one saturated constraint under an assumption checked only for the constraints known at the time. Here, it is proved for every generalized Pauli constraint, with no assumption, and also in the spin-adapted setting. The rule can only fail for the ordering constraints ${\lambda }_j\ge {\lambda }_{j+1}$. Several saturated constraints are served by one basis whenever their common zero face contains a non-degenerate point. In practice, occupation numbers are quasipinned rather than pinned, and the rule survives with an explicit error bound.

arXiv comment28 pages, 1 figure