The Structure of the Density-Potential Mapping. Part II: Including Magnetic Fields

TheHohenberg−Kohntheoremof density-functionaltheory(DFT)is broadlyconsideredtheconceptualbasisfora fullcharacterizationof an electronicsystemin its groundstateby justone-bodyparticledensity.In thisPartII of a seriesof twoarticles,weaimat clarifyingthestatusof thistheoremwithindifferentextensionsofDFTincludingmagneticfields.Wewillin particulardiscusscurrent-density-functionaltheory(CDFT)andreviewthedifferentformulationsknownintheliterature,includingtheconventionalparamagneticCDFTandsomenonstandardalternatives.Fortheformer,it is knownthattheHohenberg−Kohntheoremis nolongervaliddueto counterexamples.Nonetheless,paramagneticCDFThasthemathematicalframeworkclosestto standardDFTand,justlikein standardDFT,nondifferentiabilityof thedensityfunctionalcanbe mitigatedthroughMoreau−Yosidaregularization.Interestinginsightscanbe drawnfrombothMaxwell−SchrödingerDFTandquantum-electrodynamicDFT,whicharealsodiscussedhere.