  We construct a local interacting quantum dimer model on the square lattice,
whose zero-temperature phase diagram is characterized by a line of critical
points separating two ordered phases of the valence bond crystal type. On one
side, the line of critical points terminates in a quantum transition inherited
from a Kosterlitz-Thouless transition in an associated classical model. We also
discuss the effect of a longer-range dimer interactions that can be used to
suppress the line of critical points by gradually shrinking it to a single
point. Finally, we propose a way to generalize the quantum Hamiltonian to a
dilute dimer model in presence of monomers and we qualitatively discuss the
phase diagram.
