Universality of the one dimensional Bose gas with delta interaction
  We consider several models of interacting bosons in a one dimensional lattice. Some of them are not integrable like the Bose-Hubbard others are integrable. At low density all of these models can be described by the Bose gas with delta interaction. The lattice corrections corresponding to the different models are contrasted. 
Luigi Amico and Vladimir Korepin