  Substituting magnetic ions with nonmagnetic ions is a new way to study
dilution. Using determinant quantum Monte Carlo calculations, we investigate an
interacting Dirac fermion model with the on-site Coulomb repulsion being
randomly zero on a fraction $x$ of sites. Based on conductivity, density of
states and antiferromagnetic structure factor, our results reveal a novel
intermediate insulating phase induced by the competition between dilution and
repulsion. With increasing doping level of nonmagnetic ions, this nonmagnetic
intermediate phase is found to emerge from the zero-temperature quantum
critical point separating a metallic and a Mott insulating phase, whose
robustness is proven over a wide range of interactions. Under the premise of
strongly correlated materials, we suggest that doping nonmagnetic ions can
effectively convert the system back to the paramagnetic metallic phase. This
result not only agrees with experiments on the effect of dilution on magnetic
order but also provides a possible direction for studies focusing on the
metal-insulator transition in honeycomb lattice like materials.
