Quasi-pinning and entanglement in the lithium isoelectronic series

TL;DR

This paper investigates the near-saturation of generalized Pauli constraints in lithium atoms, revealing quasi-pinning phenomena and new saturation conditions in natural occupation numbers.

Contribution

It provides the first numerical analysis of generalized Pauli constraints in real atoms, demonstrating quasi-pinning and identifying saturation conditions in lithium.

Findings

Inequalities are nearly saturated or quasi-pinned in lithium.

Rank-six and rank-seven approximations show deviations smaller than lowest occupancy.

Rank-eight approximation reveals well-defined saturation families.

Abstract

The Pauli exclusion principle gives an upper bound of 1 on the natural occupation numbers. Recently there has been an intriguing amount of theoretical evidence that there is a plethora of additional generalized Pauli restrictions or (in)equalities, of kinematic nature, satisfied by these numbers. Here for the first time a numerical analysis of the nature of such constraints is effected in real atoms. The inequalities are nearly saturated, or quasi-pinned. For rank-six and rank-seven approximations for lithium, the deviation from saturation is smaller than the lowest occupancy number. For a rank-eight approximation we find well-defined families of saturation conditions.