A toolbox of spin-adapted generalized Pauli constraints

TL;DR

This paper develops a toolbox leveraging spin symmetry to efficiently study generalized Pauli constraints in few-electron systems, revealing that quasipinning often results from spin symmetries and simplifying wave function structures.

Contribution

It introduces a method to compute spin-adapted GPCs for larger systems and proves a superselection rule linking GPC saturation to wave function simplification.

Findings

GPCs can be computed for larger systems using spin symmetry.

Quasipinning often arises from spin symmetries rather than other effects.

Wave functions simplify significantly when GPCs are saturated or nearly saturated.

Abstract

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.