Geometry of Degeneracy in Potential and Density Space
Penz, M., & van Leeuwen, R. (2023). Geometry of Degeneracy in Potential and Density Space. Quantum, 7, Article 918. https://doi.org/10.22331/q-2023-02-09-918
© Authors, 2023
In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs. Here, we demonstrate that this only occurs at very peculiar and rare densities, those where density sets arising from degenerate ground states, called degeneracy regions, touch each other or the boundary of the whole density domain. Degeneracy regions are shown to generally be in the shape of the convex hull of an algebraic variety, even in the continuum setting. The geometry arising between density regions and the potentials that create them is analyzed and explained with examples that, among other shapes, feature the Roman surface.
PublisherVerein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
ISSN Search the Publication Forum2521-327X
Publication in research information system
MetadataShow full item record
Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF
Additional information about fundingR. v. L. further acknowledges the Academy of Finland for support under project no. 317139.
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