Bose-Hubbard model with random impurities: Multiband and nonlinear   hopping effects
  We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as, the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points however, cease to exists after the addition of the hopping disorder. 
Julia Stasi\'nska, Mateusz {\L}\k{a}cki, Omjyoti Dutta, Jakub   Zakrzewski, and Maciej Lewenstein
cond-mat.quant-gas cond-mat.dis-nn