Exact and LDA entanglement of tailored densities in an interacting one-dimensional electron system

TL;DR

This paper compares exact and LDA-based potentials and densities in a one-dimensional two-electron system, analyzing differences in energies, potentials, and spatial entanglement to evaluate the accuracy of density-functional approximations.

Contribution

It introduces a method to compute the exact potential for a tailored density in an interacting 1D electron system and compares it with LDA results, including entanglement analysis.

Findings

LDA densities and energies closely match exact results for certain conditions.

The interacting-LDA potential differs from the exact potential, highlighting approximation limitations.

Spatial entanglement varies between the exact and LDA-based systems, indicating differences in quantum correlations.

Abstract

We calculate the `exact' potential corresponding to a one-dimensional interacting system of two electrons with a specific, tailored density. We use one-dimensional density-functional theory with a local-density approximation (LDA) on the same system and calculate densities and energies, which are compared with the `exact' ones. The `interacting-LDA system' corresponding to the LDA density is then found and its potential compared with the original one. Finally we calculate and compare the spatial entanglement of the electronic systems corresponding to the interacting-LDA and original interacting system.