Confirmation of the PPLB derivative discontinuity: Exact chemical potential at finite temperatures of a model system

TL;DR

This paper confirms the PPLB derivative discontinuity model's accuracy at finite temperatures using the Hubbard dimer, extending it to improve free energy calculations relevant for warm dense matter.

Contribution

It validates the PPLB model for the Hubbard dimer at finite temperatures and extends it with corrections for better free energy estimates.

Findings

Exact agreement at zero temperature.

Model remains accurate over a range of temperatures.

Extended model improves free energy calculations.

Abstract

The landmark 1982 paper of Perdew, Parr, Levy, and Balduz (often called PPLB) laid the foundation for our modern understanding of the role of the derivative discontinuity in density functional theory, which drives much development to account for its effects. A simple model for the chemical potential at vanishing temperature played a crucial role in their argument. We investigate the validity of this model in the simplest non-trivial system to which it can be applied and which can be easily solved exactly, the Hubbard dimer. We find exact agreement in the crucial zero-temperature limit, and show the model remains accurate for a significant range of temperatures. We identify how this range depends on the strength of correlations. We extend the model to approximate free energies accounting for the derivative discontinuity, a feature missing in standard semi-local approximations. We provide a correction to this approximation to yield even more accurate free energies. We discuss the relevance of these results for warm dense matter.