  The Haldane model is a paradigmatic 2d lattice model exhibiting the integer
quantum Hall effect. We consider an interacting version of the model, and prove
that for short-range interactions, smaller than the bandwidth, the Hall
conductivity is quantized, for all the values of the parameters outside two
critical curves, across which the model undergoes a `topological' phase
transition: the Hall coefficient remains integer and constant as long as we
continuously deform the parameters without crossing the curves; when this
happens, the Hall coefficient jumps abruptly to a different integer. Previous
works were limited to the perturbative regime, in which the interaction is much
smaller than the bare gap, so they were restricted to regions far from the
critical lines. The non-renormalization of the Hall conductivity arises as a
consequence of lattice conservation laws and of the regularity properties of
the current-current correlations. Our method provides a full construction of
the critical curves, which are modified (`dressed') by the electron-electron
interaction. The shift of the transition curves manifests itself via apparent
infrared divergences in the naive perturbative series, which we resolve via
renormalization group methods.
