Implications of pinned occupation numbers for natural orbital expansions. II: Rigorous derivation and extension to non-fermionic systems

Abstract

We have explained and comprehensively illustrated in Part I that the generalized Pauli constraints suggest a natural extension of the concept of active spaces. In the present Part II, we provide rigorous derivations of the theorems involved therein. This will offer in particular deeper insights into the underlying mathematical structure and will explain why the saturation of generalized Pauli constraints implies a specific simplified structure of the corresponding many-fermion quantum state. Moreover, we extend the results of Part I to non-fermionic multipartite quantum systems, revealing that extremal single-body information has always strong implications for the multipartite quantum state. In that sense, our work also confirms that pinned quantum systems define new physical entities and the presence of pinnings reflect the existence of (possibly hidden) ground state symmetries.

arXiv commentPart II of arXiv:1908.10938

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Cited by in corpus (5)

• A complete hierarchy for the pure state marginal problem in quantum mechanics
• Refining and relating fundamentals of functional theory
• A toolbox of spin-adapted generalized Pauli constraints
• Refining ensemble $N$-representability of one-body density matrices from partial information
• Solving one-body ensemble N-representability problems with spin