Erratum: Luttinger liquid physics and spin-flip scattering on helical edges [Phys. Rev. B 85, 081106(R) (2012)]

Figure 1

Projective continuous-time quantum Monte Carlo (CTQMC) results for the Kane-Mele model with a Hubbard interaction at the edge. (a) Real-space correlations $S^{xx}(r=L/2)$ as a function of system size $L$ at different $U/\lambda$, normalized to 1 at $r=1$ for comparison. The log-log plot reveals a power law with an interaction dependent exponent $\eta =2K$. (b) $S^{xx}(q=0)/L$ as a function of $1/L$, demonstrating the absence of long-range order. Lines are fits to the form $S^{xx}(q=0)/L=b/L+c/L^{\eta }$, with $\eta$ taken from (a). Data in (a) and (b) are extrapolated to $\theta =\infty$. (c) Luttinger liquid parameter $K$ as extracted from fits to the form $S^{xx}\left(r\right)=a/r^{\eta }$ that are shown as lines in (a), and velocity $v$ as estimated from the density structure factor $N(q=2\pi /L,\tau )$ and finite-size extrapolation.

Figure 2

Single-particle spectral function $A(k,\omega )$ from projector-CTQMC simulations for $L=20$, $\theta t=80$ and (a) $U/\lambda =8$, (b) $U/\lambda =40$.

Figure 3

Luttinger parameter $K$, and spectral weight $Z$ from fits to the density structure factor $N(q,\tau )$ at $\theta t=80$ and finite-size scaling.