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The recent detailed study of quasi-one-dimensional iron-based ladders, withthe $3d$ iron electronic density $n = 6$, has unveiled surprises, such asorbital-selective phases. However, similar studies for $n=6$ iron chains arestill rare. Here, a three-orbital electronic Hubbard model was constructed tostudy the magnetic and electronic properties of the quasi-one-dimensional $n=6$iron chain Ce$_2$O$_2$FeSe$_2$, with focus on the effect of doping.Specifically, introducing the Hubbard $U$ and Hund $J_{H}$ couplings andstudying the model via the density matrix renormalization group, we report theground-state phase diagram varying the electronic density away from $n=6$. Forthe realistic Hund coupling $J_{H}/U = 1/4$, several electronic phases wereobtained, including a metal, orbital-selective Mott, and Mott insulatingphases. Doping away from the parent phase, the competition of many tendenciesleads to a variety of magnetic states, such as ferromagnetism, as well asseveral antiferromagnetic and magnetic "block" phases. In the hole-dopingregion, two different interesting orbital-selective Mott phases were found:OSMP1 (with one localized orbital and two itinerant orbitals) and OSMP2 (withtwo localized orbitals and one itinerant orbital). Moreover, chargedisproportionation phenomena were found in special doping regions. We arguethat our predictions can be tested by simple modifications in the originalchemical formula of Ce$_2$O$_2$FeSe$_2$.

physical review. b./physical review. b

Prediction of orbital selective Mott phases and block magnetic states in  the quasi-one-dimensional iron chain Ce$_2$O$_2$FeSe$_2$ under hole and  electron doping