  In this paper, we studied a generalized Bose-Hubbard model on a checkerboard
lattice with topologically nontrivial flat-band. We used mean-field method to
decouple the model Hamiltonian and obtained phase diagram by Landau theory of
second-order phase transition. We further calculate the energy gap and the
dispersion of quasi-particle or quasi-hole in Mott insulator state and found
that in strong interaction limit the quasi-particles or the quasi-holes also
have flat bands.
