  We study the edge transport properties of $2d$ interacting Hall systems,
displaying single-mode chiral edge currents. For this class of many-body
lattice models, including for instance the interacting Haldane model, we prove
the quantization of the edge charge conductance and the bulk-edge
correspondence. Instead, the edge Drude weight and the edge susceptibility are
interaction-dependent; nevertheless, they satisfy exact universal scaling
relations, in agreement with the chiral Luttinger liquid theory. Moreover,
charge and spin excitations differ in their velocities, giving rise to the
spin-charge separation phenomenon. The analysis is based on exact
renormalization group methods, and on a combination of lattice and emergent
Ward identities. The invariance of the emergent chiral anomaly under the
renormalization group flow plays a crucial role in the proof.
