Year: 2026
Type: preprint
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 $λ_j\geλ_{j+1}$. 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.
Source: arXiv (Cornell University)
Author: Reuvers, Robin
Institution: Roma Tre University
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213901532