Correlation effects in quantum spin Hall states: a Quantum Monte Carlo study

We consider a quantum spin hall insulator as realized by the Kane-Mele model with spin orbit coupling $\lambda$ supplemented by a Hubbard $U$ term. On the basis of projective auxiliary field quantum Monte Carlo simulations on lattice sizes up to $ 12 \times 12 $, we map out the magnetic phase diagram. Beyond a critical value of $U> U_c$ the quantum spin Hall insulating state is unstable towards magnetic ordering. At $U < U_c$ we study the spin, charge and single particle dyanmics of the helical edge state by retaining the Hubbard interactions only on the edge of a ribbon. As $U_c$ is approached we observe a substantial depletion of low-lying spectral weight in the dynamical charge structure factor, and a robust signature of the helical edge state in the single particle spectral function.