Kinetic quantum phase transition in bosonic superfluids on a lattice

It has been well known that quantum fluctuations induce a macroscopic phase transition from a superfluid to a Mott insulator phase driven by the repulsive potential energy in the ground state of dense bosonic systems on a lattice. We find a quantum phase transition from the homogeneous to an inhomogeneous Bose-condensate strongly affected or sometimes driven by the kinetic energy dispersion in dilute bosonic superfluids, which provides a clear identification of the superfluid state.