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

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 For the former, it is known that the Hohenberg-Kohn theorem is no longer valid due to counterexamples.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-Schrödinger DFT and quantum-electrodynamical DFT, which are also discussed here.

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Cited by in corpus (8)

• Cavity engineering of solid-state materials without external driving
• A Snapshot of Time-Dependent Density-Functional Theory
• Exchange energies with forces in density-functional theory
• Quantum-Electrodynamical Density-Functional Theory Exemplified by the Quantum Rabi Model
• Density-functional theory for the Dicke Hamiltonian
• Physical spin torques from exactly constrained exchange-correlation torques
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory
• Density-Functional Tight Binding Meets Maxwell: Unraveling the Mysteries of (Strong) Light-Matter Coupling Efficiently