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We consider a model of spinful fermions on the triangular lattice whichexhibits a C=2 Chern insulator (CI) phase with a quantized anomalous Halleffect, sandwiched between two normal insulator (NI) phases. The first NI-CIquantum phase transition is driven by simultaneous mass inversion of a pair ofDirac fermions, with short range interactions being perturbatively irrelevant.The second CI-NI transition is driven by a single quadratic band touching pointprotected by momentum space topology and C_6 lattice symmetry. A one-looprenormalization group analysis shows that short range interactions lead to asingle marginally relevant perturbation at this transition. We obtain the meanfield phase diagram of this model incorporating weak repulsive Hubbardinteractions, finding an emergent nematic dome around this CI-NI topologicalphase transition. We discuss the crossovers in the anomalous Hall conductivityat nonzero temperature, and the Landau theory of the quantum and thermaltransitions out of the nematic phase. Our results may be relevant toferromagnetic double perovskite films with spin-orbit coupling which have beenproposed to host such a NI-CI transition. Our work provides perhaps thesimplest example of an emergent phase near a quantum phase transition.

Emergent dome of nematic order around a quantum anomalous Hall critical point