In this talk, I will present a
model where the tunnelling coefficient of bosons between neighboring sites
depends on the state of 1/2-spin particles sitting on the links. The phase
diagram is analyzed using DMRG, finding non-trivial phases, including spin wave
insulators and solitonic phases, where the translational invariant symmetry is
broken in different manners. Finally, I will show how this model can be
implemented using ultracold atoms interacting with fixed impurities, which can
be simulated with trapped ions or neutral atoms.