Density-Wavefunction Mapping in Degenerate Current-Density-Functional Theory

Abstract

We show that the particle density, $\rho (\mathbf{r})$, and the paramagnetic current density, ${\mathbf{j}}^p(\mathbf{r})$, are not sufficient to determine the set of degenerate ground-state wave functions. This is a general feature of degenerate systems where the degenerate states have different angular momenta. We provide a general strategy for constructing Hamiltonians that share the same ground state density, yet differ in degree of degeneracy. We then provide a fully analytical example for a noninteracting system subject to electrostatic potentials and uniform magnetic fields. Moreover, we prove that when $(\rho ,{\mathbf{j}}^p)$ is ensemble $(v,\mathbf{A})$-representable by a mixed state formed from $r$ degenerate ground states, then any Hamiltonian $H(v^{\prime },{\mathbf{A}}^{\prime })$ that shares this ground state density pair must have at least $r$ degenerate ground states in common with $H(v,\mathbf{A})$. Thus, any set of Hamiltonians that shares a ground-state density pair $(\rho ,{\mathbf{j}}^p)$ by necessity has at least have one joint ground state.

References in corpus (3)

• Uniform magnetic fields in density-functional theory
• Degenerate ground states and nonunique potentials: breakdown and restoration of density functionals
• Density-functional theory for internal magnetic fields

Cited by in corpus (8)

• Force Balance Approach for Advanced Approximations in Density Functional Theories
• Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• The structure of the density-potential mapping. Part II: Including magnetic fields
• Geometry of Degeneracy in Potential and Density Space
• Unique Continuation for the Magnetic Schrödinger Equation
• Revisiting density-functional theory of the total current density
• Physical spin torques from exactly constrained exchange-correlation torques