Generalized Pauli constraints in small atoms

TL;DR

This paper investigates the role of generalized Pauli constraints in small atoms, revealing they are not exactly saturated but close, implying these constraints influence wave-function structure more than system behavior.

Contribution

The study applies advanced numerical methods to small atoms, showing that generalized Pauli constraints are near-saturated but not exact, impacting wave-function approximations.

Findings

Constraints are close to, but not exactly on, the boundary.

Wave-function expansions can be effectively approximated with few Slater determinants.

Results challenge the idea that constraints solely dictate system behavior.

Abstract

The natural occupation numbers of fermionic systems are subject to non-trivial constraints, which include and extend the original Pauli principle. A recent mathematical breakthrough has clarified their mathematical structure and has opened up the possibility of a systematic analysis. Early investigations have found evidence that these constraints are exactly saturated in several physically relevant systems, e.g., in a certain electronic state of the Beryllium atom. It has been suggested that in such cases, the constraints, rather than the details of the Hamiltonian, dictate the system's qualitative behaviour. Here, we revisit this question with state-of-the-art numerical methods for small atoms. We find that the constraints are, in fact, not exactly saturated, but that they lie much closer to the surface defined by the constraints than the geometry of the problem would suggest. While the results seem incompatible with the statement that the generalized Pauli constraints drive the behaviour of these systems, they suggest that the qualitatively correct wave-function expansions can in some systems already be obtained on the basis of a limited number of Slater determinants, which is in line with numerical evidence from quantum chemistry.