Energy densities in the strong-interaction limit of density functional theory

TL;DR

This paper explores the energy densities in the strong-interaction limit of density functional theory, deriving exact expressions, comparing with approximations, and analyzing implications for exchange-correlation functionals.

Contribution

It provides an exact expression for energy densities in the strong-interaction limit within a specific gauge and compares these with existing approximations and bounds.

Findings

Exact energy densities derived for small atoms and quantum dots.

Comparison shows differences between exact results and approximations.

Insights into the local Lieb-Oxford bound and its implications.

Abstract

We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small atoms and small model quantum dots are compared with available approximations defined in the same gauge. The idea of a local interpolation along the adiabatic connection is discussed, comparing the energy densities of the Kohn-Sham, the physical, and the strong-interacting systems. We also use our results to analyze the local version of the Lieb-Oxford bound, widely used in the construction of approximate exchange-correlation functionals.