Insulator-bad metal transition in RNiO$_3$ nickelates beyond the hubbard model and density functional theory

The insulator-bad metal transition observed in the Jahn-Teller magnets orthonickelates RNiO$_3$ (R = rare earth or yttrium Y) is considered to be a canonical example of the Mott transition, traditionally described in the framework of the Hubbard $U-t$-model and the density functional theory. However, actually the real insulating phase of nickelates is the result of charge disproportionation (CD) with the formation of a system of spin-triplet ($S = 1$) electron [NiO$_6$]$^{10-}$ and spinless ($S = 0$) hole [NiO$_6$]$^{8-}$ centers, equivalent to a system of effective spin-triplet composite bosons moving in a nonmagnetic lattice. Taking account of only charge degree of freedom we develop a novel minimal $U-t-t_b$-model for nickelates making use of the charge triplet model with the pseudospin formalism and effective field approximation. We show the existence of two types of CD-phases, high-temperature classical CO-phase with the $G$-type charge ordering of electron and hole centers, and low-temperature quantum CDq-phase with charge and spin density transfer between electron and hole centers, uncertain valence and spin value for NiO$_6$ centers. Model $T-R$ phase diagram reproduces main features of the phase diagram found for RNiO$_3$.