  We construct a generalized quantum dimer model on two-dimensional
nonbipartite lattices including the triangular lattice, the star lattice and
the kagome lattice. At the Rokhsar-Kivelson (RK) point, we obtain its exact
ground states that are shown to be a fully gapped quantum spin liquid with the
double-semion topological order. The ground-state wave function of such a model
at the RK point is a superposition of dimer configurations with a nonlocal sign
structure determined by counting the number of loops in the transition graph.
We explicitly demonstrate the double-semion topological order in the ground
states by showing the semionic statistics of monomer excitations. We also
discuss possible implications of such double-semion resonating valence bond
states to candidate quantum spin-liquid systems discovered experimentally and
numerically in the past few years.
