The Relationship Between Entanglement, Energy, and Level Degeneracy in Two-Electrons Systems

TL;DR

This paper investigates how entanglement in two-electron systems relates to energy and degeneracy, using perturbation theory to uncover universal physical principles behind observed entanglement behaviors.

Contribution

It introduces a perturbative analysis that explains the physical origin of entanglement trends in two-electron models, highlighting their universal aspects.

Findings

Entanglement increases with energy in two-electron systems.

Excited states can have non-zero entanglement even with negligible interaction.

Perturbative approach reveals the physical mechanisms behind entanglement properties.

Abstract

The entanglement properties of two-electron atomic systems have been the subject of considerable research activity in recent years. These studies are still somewhat fragmentary, focusing on numerical computations on particular states of systems such as Helium, or on analytical studies of model-systems such as the Moshinsky atom. Some general trends are beginning to emerge from these studies: the amount of entanglement tends to increase with energy and, in the case of excited states, entanglement does not necessarily tend to zero in the limit of vanishing interaction between the two constituting particles. A physical explanation of these properties, shared by the different two-electrons models investigated so far, is still lacking. As a first step towards this goal we perform here, via a perturbative approach, an analysis of entanglement in two-electrons models that sheds new light on the physical origin of the aforementioned features and on their universal character.