Solvable Haldane Hubbard model at Falicov-Kimball limit with Topological Phase Transition

In this talk, we present a spin dependent Haldane model with Hubbard onsite interaction. In the limit when the model is reduced to the exactly solvable Falicov-Kimball model (FKM) [1], we find an interaction driven topological phase transition and a solitonic excitation with bound particle in the topological trivial region. Deviated from FKM limit, we solve this model with a mean-field approach where the Chern number phase diagram with respect to interaction is obtained. Experimentally, this model can be realized in cold atom system with imbalanced left and right circular light[2]. More generally, we explore three classes of models that can be mapped to FKM at certain symmetric point. In strong interacting limit, we found these models can be described by some effective classical Ising models.
[1] L. M.Falicov, J. C. Kimball, Phys. Rev. Lett. 22, 997(1969)
[2] W.V.Liu, F.Wilczek, and P.Zoller, Phys.Rev.A. 70, 033603(2004)