  We study phase diagrams of a class of doped quantum dimer models on the
square lattice with ground-state wave functions whose amplitudes have the form
of the Gibbs weights of a classical doped dimer model. In this dimer model,
parallel neighboring dimers have attractive interactions, whereas neighboring
holes either do not interact or have a repulsive interaction. We investigate
the behavior of this system via analytic methods and by Monte Carlo
simulations. At zero doping, we confirm the existence of a Kosterlitz-Thouless
transition from a quantum critical phase to a columnar phase. At low hole
densities we find a dimer-hole liquid phase and a columnar phase, separated by
a phase boundary which is a line of critical points with varying exponents. We
demonstrate that this line ends at a multicritical point where the transition
becomes first order and the system phase separates. The first-order transition
coexistence curve is shown to become unstable with respect to more complex
inhomogeneous phases in the presence of direct hole-hole interactions. We also
use a variational approach to determine the spectrum of low-lying density
fluctuations in the dimer-hole fluid phase.
