Effects of Interaction on Quantum Spin Hall Insulators

We study the S(z)-conserving quantum spin Hall insulator in the presence of Hubbard U from a field theory point of view. The main findings are the following. (1) For arbitrarily small U the edges possess power-law correlated antiferromagnetic XY local moments. Gapless charge excitations arise from the Goldstone-Wilczek mechanism. (2) Electron tunneling between opposite edges allows vortex instantons to proliferate when K, the XY stiffness constant, satisfies 4 pi K + (4 pi K)(-1) < 4. When the preceding inequality is violated, the edge modes remain gapless despite the sample width being finite. (3) The phase transition from the topological insulator to the large U antiferromagnetic insulator is triggered by the condensation of magnetic excitons. (4) In the large U antiferromagnetic insulating phase the magnetic vortices carry charges proportional to the square magnitude of the antiferromagnetic order parameter.