On the lower bound on the exchange-correlation energy in two dimensions

TL;DR

This paper analyzes the lower bound of exchange-correlation energy in two-dimensional systems, deriving a simple density-functional form, and investigates how system geometry influences the bound's tightness.

Contribution

It provides a simplified density-functional expression for the lower bound and explores geometric factors affecting its proximity in finite systems.

Findings

Circular geometry and weak confining potential lead to closer approach to the bound

Derived explicit prefactor for the lower bound

High-density limit analysis supports geometric influence on the bound

Abstract

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature.