Entanglement and density-functional theory: testing approximations on Hooke's atom

TL;DR

This paper introduces two new methods within density-functional theory to calculate spatial entanglement in an interacting electron system, tested on Hooke's atom, and compares their accuracy with exact results and perturbation methods.

Contribution

The paper develops and tests two novel DFT-based methods for calculating spatial entanglement, providing insights into their accuracy and applicability.

Findings

Methods accurately reproduce exact entanglement trends

Entanglement varies with confining potential strength

New methods outperform standard perturbation approaches

Abstract

We present two methods of calculating the spatial entanglement of an interacting electron system within the framework of density-functional theory. These methods are tested on the model system of Hooke's atom for which the spatial entanglement can be calculated exactly. We analyse how the strength of the confining potential affects the spatial entanglement and how accurately the methods that we introduced reproduce the exact trends. We also compare the results with the outcomes of standard first-order perturbation methods. The accuracies of energies and densities when using these methods are also considered.