2024/12/02 by Julia Liebert, Federico Castillo, Liebert, Julia +7 · 1 citation
Biochemistry, Genetics and Molecular Biology · #Fractal and DNA sequence analysis
paper · doi:10.48550/arxiv.2412.01805
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 \boldsymbol 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(\boldsymbol 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.