  A family of the pair hopping models exhibiting the incompressible quantum
liquid at fractional filling $1/m^D$ is constructed in $D$ dimensional lattice.
Except in one dimension, the lattice is the generalized edge-shared triangular
lattice, for example the triangular lattice in two dimensions and tetrahedral
lattice in three dimensions. They obey the new symmetry, conservation of the
center-of-mass position proposed by Seidel et al..\cite{Seidel2005} The
uniqueness of the ground state is proved rigorously in the open boundary
condition. The finiteness of the excitation energy is calculated by the single
mode approximation.
