Featureless Mott Insulators

A family of the pair hopping models exhibiting the incompressible quantum liquid at fractional filling $1\mathrm{/}{m}^D$ 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.