Spin Hall insulators beyond the Helical Luttinger model

TL;DR

This paper rigorously proves the quantization of edge spin conductance in an extended Kane-Mele-Hubbard model, incorporating lattice effects beyond the Helical Luttinger model, using advanced renormalization group techniques.

Contribution

It establishes the exact quantization of edge spin conductance and validates Helical Luttinger liquid relations beyond the usual approximation, accounting for lattice effects.

Findings

Quantization of edge spin conductance is rigorously proven.

Helical Luttinger relations hold beyond the standard approximation.

Lattice effects are essential for universality in the model.

Abstract

We consider the interacting, spin conserving, extended Kane-Mele-Hubbard model, and we 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 fully takes 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 allow to relate the emergent chiral anomaly with the finite renormalizations due to lattice corrections.