Toolbox of spin-adapted generalized Pauli constraints

Julia, Liebert; Yannik, Lemke; Murat, Altunbulak; Tomasz, Maciazek; Christian, Ochsenfeld; Schilling, Christian (2025): Toolbox of spin-adapted generalized Pauli constraints. Physical Review Research, 7: 023247. ISSN 2643-1564

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.

• Doc-Type: Article (LMU)
• Organisational unit (Faculties): 17 Physics
• DFG subject classification of scientific disciplines: Natural sciences
• DFG: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 414324924
• DFG: Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 491502892