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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 derivativediscontinuity in density functional theory, which drives much development toaccount for its effects. A simple model for the chemical potential at vanishingtemperature played a crucial role in their argument. We investigate thevalidity of this model in the simplest non-trivial system to which it can beapplied and which can be easily solved exactly, the Hubbard dimer. We findexact agreement in the crucial zero-temperature limit, and show the modelremains accurate for a significant range of temperatures. We identify how thisrange depends on the strength of correlations. We extend the model toapproximate free energies accounting for the derivative discontinuity, afeature missing in standard semi-local approximations. We provide a correctionto this approximation to yield even more accurate free energies. We discuss therelevance of these results for warm dense matter.

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