Correlation Effects in Quantum Spin Hall Insulators: a Quantum Monte Carlo Study
We consider the Kane-Mele model with spin-orbit coupling supplemented by a Hubbard U term. On the basis of projective auxiliary field quantum Monte Carlo simulations on lattice sizes up to 12 x 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 spin, charge and single-particle dynamics of the helical Luttinger liquid by retaining the Hubbard interaction only on the edge of a ribbon. Correlation effects greatly suppress charge currents along the edge whereas spin currents remain robust.