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

• Main Authors: Seidl, Michael, Benyahia, Tarik, Kooi, Derk P., Gori-Giorgi, Paola
• Format: Report
• Language: unknown
• Published: arXiv 2022
• Subjects: Chemical Physics physics.chem-ph; Strongly Correlated Electrons cond-mat.str-el; FOS Physical sciences; Rupert; Elliott; Ari; Mathieu; laptev
• Online Access: https://dx.doi.org/10.48550/arxiv.2202.10800; https://arxiv.org/abs/2202.10800

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. : Submitted to the book in honor of Elliott Lieb's 90th birthday, edited by Rupert L. Frank, Ari Laptev, Mathieu Lewin and Robert Seiringer, published by EMS Press. Revised version where we have updated fig. 1.1 and table 1.2 to include a very recent improvement on the upper bound for the optimal constant (published in arXiv:2203.12473)