  We consider a model of spinful fermions on the triangular lattice which
exhibits a C=2 Chern insulator (CI) phase with a quantized anomalous Hall
effect, sandwiched between two normal insulator (NI) phases. The first NI-CI
quantum phase transition is driven by simultaneous mass inversion of a pair of
Dirac fermions, with short range interactions being perturbatively irrelevant.
The second CI-NI transition is driven by a single quadratic band touching point
protected by momentum space topology and C_6 lattice symmetry. A one-loop
renormalization group analysis shows that short range interactions lead to a
single marginally relevant perturbation at this transition. We obtain the mean
field phase diagram of this model incorporating weak repulsive Hubbard
interactions, finding an emergent nematic dome around this CI-NI topological
phase transition. We discuss the crossovers in the anomalous Hall conductivity
at nonzero temperature, and the Landau theory of the quantum and thermal
transitions out of the nematic phase. Our results may be relevant to
ferromagnetic double perovskite films with spin-orbit coupling which have been
proposed to host such a NI-CI transition. Our work provides perhaps the
simplest example of an emergent phase near a quantum phase transition.
