Liebert, Julia, Castillo, Federico, Labbé, Jean-Philippe, Maciazek, Tomasz et Schilling, Christian.
2025.
« Solving one-body ensemble N-representability problems with spin ».
Quantum, vol. 9.
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Résumé
The Pauli exclusion principle is fundamental to understanding electronic quantum systems. It namely constrains the expected occupancies ni of orbitals φi according to 0≤ni≤2. In this work, we first refine the underlying one-body N-representability problem by taking into account simultaneously spin symmetries and a potential degree of mixedness w of the N-electron quantum state. We then derive a comprehensive solution to this problem by using basic tools from representation theory, convex analysis and discrete geometry. Specifically, we show that the set of admissible orbital one-body reduced density matrices is fully characterized by linear spectral constraints on the natural orbital occupation numbers, defining a convex polytope ΣN,S(w)⊂[0,2]d. These constraints are independent of M and the number d of orbitals, while their dependence on N,S is linear, and we can thus calculate them for arbitrary system sizes and spin quantum numbers. Our results provide a crucial missing cornerstone for ensemble density (matrix) functional theory.
| Type de document: | Article publié dans une revue, révisé par les pairs |
|---|---|
| Professeur: | Professeur Labbé, Jean-Philippe |
| Affiliation: | Département des enseignements généraux |
| Date de dépôt: | 23 déc. 2025 17:12 |
| Dernière modification: | 10 janv. 2026 18:57 |
| URI: | https://espace2.etsmtl.ca/id/eprint/33160 |
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