  Extended Bose Hubbard models with nearest neighbour interaction describe
minimally the effect of long range interaction on ultra cold atoms in deep
optical lattices. Rotation of such optical lattices subject such neutral cold
atoms to the effect of an artificial magnetic field. The modification of the
phase boundaries of the density wave and Mott Insulator phases due to this
rotation are shown to be related to the edge spectrum of spinorial and scalar
Harper equation. Corresponding profiles of the checkerboard vortex states with
sublattice modulated superfluid order parameter near density wave phase
boundary are calculated.
