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Phase Diagram of the Kane-Mele-Hubbard model

Motivated by recent numerical results, we study the phase diagram of the Kane-Mele-Hubbard (KHM) model, especially the nature of its quantum critical points. The phase diagram of the Kane-Mele-Hubbard model can be understood by breaking the SO(4) symmetry of our previous work down to U(1)_spin x U(1)_charge x PH symmetry. The vortices of the inplane Neel phase carry charge, and the proliferation of the charged magnetic vortex drives the transition between the inplane Neel phase and the QSH insulator phase; this transition belongs to the 3d XY universality class. The transition between the liquid phase and the inplane Neel phase is an anisotropic O(4) transition, which eventually becomes first order due to quantum fluctuation. The liquid-QSH transition is predicted to be first order based on a 1/N calculation.