标题： 自旋适应的广义泡利约束工具箱 显示英文标题

标题： A toolbox of spin-adapted generalized Pauli constraints

摘要： 我们建立了一个工具箱，用于研究和应用少电子量子系统中的自旋适应广义泡利约束（GPCs）。通过利用实际的$N$-电子波函数的自旋对称性，底层的一体纯$N$-可表示性问题得到简化，使我们能够计算比以前可访问的更大系统尺寸的GPCs。我们随后揭示并严格证明了一种超选择规则，突显了GPCs的重要性：当自旋适应的GPC（近似）饱和时——称为（准）钉扎——相应的$N$-电子波函数会呈现出简化的结构。具体来说，在仅基于自然轨道的组态相互作用展开中，只有非常特定的自旋构型状态函数可能有贡献。为了评估（准）钉扎的非平凡性，我们引入了一种几何度量，将其与由简单（自旋适应）泡利约束引起的（准）钉扎进行对比。对少电子系统的应用表明，之前观察到的准钉扎主要源于自旋对称性。 显示英文摘要

摘要： We establish a toolbox for studying and applying spin-adapted generalized Pauli constraints (GPCs) in few-electron quantum systems. By exploiting the spin symmetry of realistic $N$-electron wave functions, the underlying one-body pure $N$-representability problem simplifies, allowing us to calculate the GPCs for larger system sizes than previously accessible. We then uncover and rigorously prove a superselection rule that highlights the significance of GPCs: whenever a spin-adapted GPC is (approximately) saturated - referred to as (quasi)pinning - the corresponding $N$-electron wave function assumes a simplified structure. Specifically, in a configuration interaction expansion based on natural orbitals only very specific spin configuration state functions may contribute. To assess the nontriviality of (quasi)pinning, we introduce a geometric measure that contrasts it with the (quasi)pinning induced by simple (spin-adapted) Pauli constraints. Applications to few-electron systems suggest that previously observed quasipinning largely stems from spin symmetries.