The Bosonic Kane-Mele Hubbard model

We investigate the bosonic equivalent of the Kane-Mele model on the honeycomb lattice [1] including spin-orbit and interaction effects. This model is a generalization of the interacting bosonic Haldane model introduced in Ref. [2]. We also allow for an on-site conversion (coherent) term between the two species. We analyze the phase diagram using bosonic dynamical mean-field theory and analytical methods. In the Mott phase, a strong-coupling expansion is performed to investigate the magnetism and frustration effects. A connection is drawn with the quantum theory of an antiferromagnet on a triangular lattice in a magnetic field [3]. This model can be realized in ultra-cold atom systems with current technology. [1] C. L. Kane and E. Mele, Phys. Rev. Lett. 95, 226801 (2005). [2] I. Vasic, A. Petrescu, K. Le Hur and W. Hofstetter, Phys. Rev. B 91, 094502 (2015). [3] A. V. Chubukov and D. I. Golosov, J. Phys. Cond. Matt. 3 69 (1991).