Nonuniqueness in spin-density-functional theory on lattices

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.