发表机构
Università degli Studi Roma Tre（罗马第三大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在无假设条件下证明了所有广义泡利约束下费米子态占据数的选择规则，并推广至自旋适配情形，同时给出了准钉扎情形下的规则形式。
AI 中文摘要
当费米子态的自然占据数饱和一个广义泡利约束时，该态遵循一条选择规则：只有那些自身饱和该约束的自然轨道构型才有贡献。因此，钉扎效应挑选出一个活性空间。该选择规则此前已在非简并占据数情形下得到证明；对于简并情形，它仅作为猜想提出，并在一个未经证实的假设下针对单个饱和约束得到证明。本文在无任何假设的情况下，对所有广义泡利约束证明了该规则，并在自旋适配情形下同样成立。该规则仅对排序约束 $\lambda_j\ge\lambda_{j+1}$ 可能失效。当多个饱和约束的公共零面包含一个非简并点时，它们可由同一基组满足。实际中，占据数通常是准钉扎而非严格钉扎，我给出了此时规则的具体形式。
英文摘要
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.
Comments28 pages, 1 figure
