  A general mechanism is presented by which topological physics arises in
strongly correlated systems without flat bands. Starting from a charge transfer
insulator, topology emerges when the charge transfer energy between the cation
and anion is reduced to invert the lower Hubbard band and the spin-degenerate
charge transfer band. A universal low-energy theory is developed for the
inversion of charge transfer gap in a quantum antiferromagnet. The inverted
state is found to be a quantum anomalous Hall (QAH) insulator with non-coplanar
magnetism. Interactions play two essential roles in this mechanism: producing
the insulating gap and quasiparticle bands prior to the band inversion, and
causing the change of magnetic order necessary for the QAH effect after
inversion. Our theory explains the electric field induced transition from
correlated insulator to QAH state in AB-stacked TMD bilayer MoTe$_2$/WSe$_2$.
