Spin Hall insulators beyond the Helical Luttinger model

We consider the interacting, spin-conserving, extended Kane-Mele-Hubbard model, andwe rigorously establish the exact quantization of the edge spin conductance and the validity of the helical Luttinger liquid relations for Drude weights and susceptibilities. Our analysis takes fully into account lattice effects, typically neglected in the helical Luttinger model approximation, which play an essential role for universality. The analysis is based on exact renormalization-group methods and on a combination of lattice and emergent Ward identities, which enable the emergent chiral anomaly to be related with the finite renormalizations due to lattice corrections.