| We report on our recent work on interaction phenomena in Chern insulators and topological insulators which can be categorized into different classes: (i) weak interactions interpreted as a perturbative correction to the kinetic theory. (ii) strong interactions described within a Mott picture where topologically ordered phases can arise from anisotropic spin exchange. (iii) strongly correlated fractional Chern phases where topological order sets in along with fractionalized excitations and finite quantum dimension. We report on recent progress on how to induce a topological band structure from fluctuation effects due to interactions which cannot be reconciled within a static mean field picture. Furthermore, we analyze the honeycomb Iridate compounds from a spin orbit Mott picture, and define a pseudo potential formalism for fractional Chern pases. |
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