Abstract
We have explained and comprehensively illustrated in Part I (Schilling et al 2019 arXiv:1908.10938) that the generalized Pauli constraints suggest a natural extension of the concept of active spaces. In the present Part I (Schilling et al 2019 arXiv:1908.10938)I, 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 (Schilling et al 2019 arXiv:1908.10938) 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.
Highlights
Equation (1) gives rise to the natural occupation numbers (NONs) nj and the natural orbitals (NOs) ∣ jñ, the corresponding eigenstates [1, 2]
In order to deduce the support of ∣Yñ from lemma 7 and the knowledge of its NONs, we have to take a closer look at the subtle structure of local symmetries of states with fixed NONs
Saturation of this universal upper bound on the degree of condensation of hard-core bosons implies that there is one natural orbital, ∣1ñ, of r1 which is maximally unbiased with respect to the lattice site basis {∣cjñ}, ácj∣1ñ = 1 d for all j, and the corresponding quantum state is given by is maximally delocalized, ∣Yñ μ åi1
Summary
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