Fermionic statistics in the strongly correlated limit of Density Functional Theory

TL;DR

This paper investigates the strong coupling limit in density functional theory, confirming theoretical predictions for two-electron systems and exploring how fermionic statistics influence the behavior at large coupling strengths.

Contribution

It compares theoretical predictions with numerical data for the strong coupling limit and studies the impact of fermionic statistics at high interaction strengths.

Findings

The two leading terms in the strong coupling limit are asymptotically exact.

Fermionic spin effects enter at orders proportional to e^{-\sqrt{ ext{lambda}}}.

Numerical results confirm theoretical predictions for two-electron systems.

Abstract

Exact pieces of information on the adiabatic connection integrand $W_{\lambda}[\rho]$, which allows to evaluate the exchange-correlation energy of Kohn-Sham density functional theory, can be extracted from the leading terms in the strong coupling limit ($\lambda\to\infty$, where $\lambda$ is the strength of the electron-electron interaction). In this work, we first compare the theoretical prediction for the two leading terms in the strong coupling limit with data obtained via numerical implementation of the exact Levy functional in the simple case of two electrons confined in one dimension, confirming the asymptotic exactness of these two terms. We then carry out a first study on the incorporation of the fermionic statistics at large coupling $\lambda$, both numerical and theoretical, confirming that spin effects enter at orders $\sim e^{-\sqrt{\lambda}}$.