Confirmation of the PPLB derivative discontinuity: Exact chemical
potential at finite temperatures of a model system
- URL: http://arxiv.org/abs/2007.03840v4
- Date: Wed, 29 Jul 2020 03:32:36 GMT
- Title: Confirmation of the PPLB derivative discontinuity: Exact chemical
potential at finite temperatures of a model system
- Authors: Francisca Sagredo, Kieron Burke
- Abstract summary: A simple model for the chemical potential at vanishing temperature played a crucial role in Perdew, Parr, Levy, and Balduz's 1982 paper.
We find exact agreement in the crucial zero-temperature limit, and show the model remains accurate for a significant range of temperatures.
We extend the model to approximate free energies accounting for the derivative discontinuity, a feature missing in standard semi-local approximations.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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