The structure of the density-potential mapping. Part II: Including magnetic fields

• URL: http://arxiv.org/abs/2303.01357v2
• Date: Sun, 30 Jul 2023 15:17:57 GMT
• Title: The structure of the density-potential mapping. Part II: Including magnetic fields
• Authors: Markus Penz, Erik I. Tellgren, Mih\'aly A. Csirik, Michael Ruggenthaler, Andre Laestadius
• Abstract summary: The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. We aim at clarifying the status of this theorem within different extensions of DFT including magnetic fields.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. In this Part~II of a series of two articles, we aim at clarifying the status of this theorem within different extensions of DFT including magnetic fields. We will in particular discuss current-density-functional theory (CDFT) and review the different formulations known in the literature, including the conventional paramagnetic CDFT and some non-standard alternatives. For the former, it is known that the Hohenberg-Kohn theorem is no longer valid due to counterexamples. Nonetheless, paramagnetic CDFT has the mathematical framework closest to standard DFT and, just like in standard DFT, non-differentiability of the density functional can be mitigated through Moreau-Yosida regularization. Interesting insights can be drawn from both Maxwell-Schr\"odinger DFT and quantum-electrodynamical DFT, which are also discussed here.

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