  There is strong interest in discovering or designing wide gap Chern
insulators. Here we follow a Chern insulator to trivial Mott insulator
transition versus interaction strength U in a honeycomb lattice Fe-based
transition metal oxide, discovering that a spin-orbit coupling energy scale
$\xi$=40 meV can produce and maintain a topologically entangled Chern
insulating state against large band structure changes arising from an
interaction strength U up to 60 times as large. Within the Chern phase the
minimum gap switches from the zone corner K to the zone center $\Gamma$ while
maintaining the topological structure. At a critical strength $U_c$, the
continuous evolution of the electronic structure encounters a gap closing then
reopening, upon which the system reverts to a trivial Mott insulating phase.
This Chern insulator phase of honeycomb lattice Fe$^{2+}$ BaFe$_2$(PO$_4$)$_2$
corresponds to a large Chern number C=-3 that will provide enhanced anomalous
Hall conductivity due to the associated three edge states threading through the
bulk gap of 80 meV.
