Density-functional theory for internal magnetic fields

Tellgren, Erik I.

doi:10.1103/physreva.97.012504

Cited by 21 publications

(62 citation statements)

References 57 publications

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“…As far as the total (physical) current density is concerned, recent work has established a density-functional theory based on the Maxwell-Schrödinger model [9]. In this theory, the potential space contains pairs x * = (v, B) of electrostatic scalar potentials and magnetic fields.…”

Section: B Current-density-functional Theoriesmentioning

confidence: 99%

Generalized Kohn–Sham iteration on Banach spaces

Laestadius

Penz

Tellgren

et al. 2018

The Journal of Chemical Physics

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A detailed account of the Kohn-Sham algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach spaces, is given here. Starting from a Levy-Lieb-type functional, its convex and lower semi-continuous extension is regularized to obtain differentiability. This extra layer allows to rigorously introduce, in contrast to the common unregularized approach, a well-defined Kohn-Sham iteration scheme. Convergence in a weak sense is then proven. This generalized formulation is applicable to a wide range of different density-functional theories and possibly even to models outside of quantum mechanics.

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Section: B Current-density-functional Theoriesmentioning

confidence: 99%

Generalized Kohn–Sham iteration on Banach spaces

Laestadius

Penz

Tellgren

et al. 2018

The Journal of Chemical Physics

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“…It is an appromimation of non-relativistic QED [12,18]. It was studied throught a DFT approach by Tellgren in [50], and the resulting framework was called Maxwell DFT. We define…”

Section: Ill-posedness Of the Hohenberg-kohn Theorem For Spin-currentmentioning

confidence: 99%

Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem

Garrigue

2018

Math Phys Anal Geom

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We prove the strong unique continuation property for manybody Pauli operators with external potentials, interaction potentials and magnetic fields in L p loc (R d ), and with magnetic potentials in L q loc (R d ), where p > max(2d/3, 2) and q > 2d. For this purpose, we prove a singular Carleman estimate involving fractional Laplacian operators. Consequently, we obtain the Hohenberg-Kohn theorem for the Maxwell-Schrödinger model.

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“…This means the usual presentations of DFT already assume some form of regularization of the functionals. Other special forms of DFT like with internal magnetic fields [20] or finite temperatures [21,22] automatically include regularization effects.…”

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confidence: 99%

Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions

et al. 2019

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The exact Kohn-Sham iteration of generalized density-functional theory in finite dimensions with a Moreau-Yosida regularized universal Lieb functional and an adaptive damping step is shown to converge to the correct ground-state density.The Kohn-Sham (KS) scheme [1] of ground-state density-functional theory (DFT) is the cornerstone of electronic structure calculations in quantum chemistry and solid-state physics [2]. It maps a complicated system of interacting electrons onto an auxiliary, non-interacting KS system. This yields a set of coupled one-particle equations that need to be solved self-consistently. Since a direct solution is unfeasible, practical approaches are variations of self-consistent field methods taking the form of fixed-point iterations or energy minimization algorithms [3][4][5][6][7][8]. To date, no method has been rigorously shown to converge to the correct ground-state density. Convergence results for approximate schemes are available for auxiliary assumptions [9], and reliably achieving convergence in systems with small band gaps or for transition metals remains a hard practical challenge [10]. Approximation techniques face the problem of an exponential growth of local minima with increasing number of particles [11]. Such local minima appear as 'false' solutions in the energy landscape and distract from the global, absolute minimum [12]. Hence, a method with mathematically guaranteed convergence to the correct minimizer is of central importance and has been listed as one of twelve outstanding problems in DFT [13].

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Density-functional theory for internal magnetic fields

Cited by 21 publications

References 57 publications

Generalized Kohn–Sham iteration on Banach spaces

Generalized Kohn–Sham iteration on Banach spaces

Unique Continuation for Many-Body Schrödinger Operators and the Hohenberg-Kohn Theorem

Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions

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