Density-functional theory for internal magnetic fields

Abstract

A density-functional theory is developed based on the Maxwell--Schrödinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and the total magnetic field, which can equivalently be represented as a physical current density. Hence, the theory can be regarded as a physical current-density functional theory and an alternative to the paramagnetic current density-functional theory due to Vignale and Rasolt. The energy functional has strong enough convexity properties to allow a formulation that generalizes Lieb's convex analysis-formulation of standard density-functional theory. Several variational principles as well as a Hohenberg--Kohn-like mapping between potentials and ground-state densities follow from the underlying convex structure. Moreover, the energy functional can be regarded as the result of a standard approximation technique (Moreau--Yosida regularization) applied to the conventional Schrödinger ground state energy, which imposes limits on the maximum curvature of the energy (w.r.t.\ the magnetic field) and enables construction of a (Fréchet) differentiable universal density functional.

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Cited by in corpus (11)

• Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions
• Force Balance Approach for Advanced Approximations in Density Functional Theories
• Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
• Generalized Kohn-Sham iteration on Banach spaces
• The structure of the density-potential mapping. Part II: Including magnetic fields
• Hohenberg-Kohn theorems for interactions, spin and temperature
• Unique continuation for many-body Schrödinger operators and the Hohenberg-Kohn theorem. II. The Pauli Hamiltonian
• Density-Wavefunction Mapping in Degenerate Current-Density-Functional Theory
• Unique Continuation for the Magnetic Schrödinger Equation
• Revisiting density-functional theory of the total current density
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory