The Lieb-Oxford bound and the optimal transport limit of DFT

TL;DR

This paper explores the relationship between the Lieb-Oxford bound in density functional theory and the optimal transport limit, highlighting historical insights and illustrating with examples how these concepts are interconnected.

Contribution

It clarifies the connection between the Lieb-Oxford inequality and the optimal transport limit in DFT, emphasizing contributions from Elliott Lieb.

Findings

The Lieb-Oxford bound relates to the optimal transport limit in DFT.

Historical insights from Elliott Lieb suggest a deep connection.

Examples illustrate the theoretical link between bounds and limits.

Abstract

We review and illustrate with several examples the connection between the search for lower bounds for the optimal constant in the Lieb-Oxford inequality and the optimal transport limit (or strictly-correlated-electrons limit) of density functional theory. We focus in particular on several contributions from Elliott Lieb which already hinted at this connection.