Mott Insulator-Superfluid Transition in a Generalized Bose-Hubbard Model   with Topologically Non-trivial Flat-Band
  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. 
Xing-Hai Zhang and Su-Peng Kou
cond-mat.quant-gas quant-ph