Symmetry-breaking polymorphous descriptions for correlated materials without interelectronic <i>U</i>

Correlated materials with open-shell $d$ and $f$ ions having degenerate band-edge states show a rich variety of interesting properties ranging from metal-insulator transition to unconventional superconductivity. The textbook view for the electronic structure of these materials is that mean-field approaches are inappropriate, as the interelectronic interaction U is required to open a band gap between the occupied and unoccupied degenerate states while retaining symmetry. We show that the latter scenario often defining what Mott insulators are is in fact not needed for the $3d$ binary oxides MnO, FeO, CoO, and NiO. The mean-field-like band theory can indeed lift such degeneracies in the binaries when nontrivial unit-cell representations (polymorphous networks) are allowed to break symmetries, in conjunction with a recently developed nonempirical exchange and correlation density functional without an on-site interelectronic interaction U. We explain how density-functional theory in the polymorphous representation achieves band-gap opening in correlated materials through a separate mechanism from the Mott-Hubbard approach. We show the method predicts magnetic moments and gaps for the four binary monoxides in both the antiferromagnetic and paramagnetic phases, offering an effective alternative to symmetry-conserving approaches for studying a range of functionalities in open $d$- and $f$-shell complex materials.