Implications of pinned occupation numbers for natural orbital expansions. I: Generalizing the concept of active spaces

TL;DR

This paper generalizes the concept of active spaces in quantum many-body systems using generalized Pauli constraints, establishing new criteria for selecting electron configurations and exploring implications for multipartite quantum states.

Contribution

It introduces a generalized framework for active spaces based on Pauli constraints and extends the concept to non-fermionic systems, revealing new physical insights.

Findings

Saturation of Pauli constraints characterizes specific active electron configurations.

Pinned quantum systems indicate the presence of ground state symmetries.

Extremal single-body information influences multipartite quantum states.

Abstract

The concept of active spaces simplifies the description of interacting quantum many-body systems by restricting to a neighbourhood of active orbitals around the Fermi level. The respective wavefunction ansatzes which involve all possible electron configurations of active orbitals can be characterized by the saturation of a certain number of Pauli constraints $0 \leq n_i \leq 1$, identifying the occupied core orbitals ($n_i=1$) and the inactive virtual orbitals ($n_j=0$). In Part I, we generalize this crucial concept of active spaces by referring to the generalized Pauli constraints. To be more specific, we explain and illustrate that the saturation of any such constraint on fermionic occupation numbers characterizes a distinctive set of active electron configurations. A converse form of this selection rule establishes the basis for corresponding multiconfigurational wavefunction ansatzes. In Part II, we provide rigorous derivations of those findings. Moroever, we extend our results 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.