Luttinger Liquid Physics and Spin-Flip Scattering on Helical Edges

We investigate electronic correlation effects on edge states of quantum spin-Hall insulators within the Kane-Mele-Hubbard model by means of quantum Monte Carlo simulations. Given the U(1) spin symmetry and time-reversal invariance, the low-energy theory is the helical Tomanaga-Luttinger model, with forward scattering only. For weak to intermediate interactions, this model correctly describes equal-time spin and charge correlations, including their doping dependence. As apparent from the Drude weight, bulk states become relevant in the presence of electron-electron interactions, rendering the forward-scattering model incomplete. Strong correlations give rise to slowly decaying transverse spin fluctuations, and inelastic spin-flip scattering strongly modifies the single-particle spectrum, leading to graphene-like edge state signatures. The helical Tomanaga-Luttinger model is completely valid only asymptotically in the weak-coupling limit.