Nonuniqueness in spin-density-functional theory on lattices

TL;DR

This paper investigates the nonuniqueness issues in spin-density-functional theory on lattices, discovering new cases and discussing their implications for the fundamental understanding of SDFT.

Contribution

The study introduces two new non-trivial cases of nonuniqueness in lattice SDFT, expanding the understanding of density-potential mappings.

Findings

Identified local saturation and global noncollinear nonuniqueness cases

Discussed properties and implications of these nonuniqueness cases

Showed that only some known nonuniqueness cases persist in the continuum limit

Abstract

In electronic many-particle systems, the mapping between densities and spin magnetizations, {n(r), m(r)}, and potentials and magnetic fields, {v(r), B(r)}, is known to be nonunique, which has fundamental and practical implications for spin-density-functional theory (SDFT). This paper studies the nonuniqueness (NU) in SDFT on arbitrary lattices. Two new, non-trivial cases are discovered, here called local saturation and global noncollinear NU, and their properties are discussed and illustrated. In the continuum limit, only some well-known special cases of NU survive.