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

TL;DR

This paper rigorously derives theorems related to generalized Pauli constraints, extending previous work to non-fermionic systems and revealing how pinning phenomena influence the structure of quantum states and symmetries.

Contribution

It provides a rigorous mathematical foundation for the implications of pinned occupation numbers and extends the theory to non-fermionic multipartite quantum systems.

Findings

Saturation of generalized Pauli constraints implies simplified quantum state structures.

Extends the concept of pinned states to non-fermionic systems.

Pinning indicates underlying ground state symmetries.

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.