of interacting classical dimers at finite hole density. This mapping to a 2D classical statistical mechanical system, for which there is a wealth of available results and methods, makes this class of problems solvable.[@rokhsar88; @moessner01a; @ardonne04; @Castelnovo06]

In this work we will investigate the behavior of doped QDMs which satisfy the RK conditions by studying the correlations encoded in their ground state wave functions. The phase diagrams of these systems turn out to be quite rich. As we shall see, these simple models can describe many aspects of the physics of interest in strongly correlated systems, including a dimer-hole liquid phase (a Bose-Einstein condensate of holes), valence-bond crystalline states, phase separation, and more general inhomogeneous phases. The undoped version of this system was studied in detail in Ref. , where a quantum phase transition was found that was argued to belong to the Kosterlitz-Thouless (KT) universality class, from a critical phase to a columnar state with long-range order. In this paper we confirm that this is indeed the case. At finite hole density, hitherto available results are limited to the form of the associated RK QDM Hamiltonian[@Castelnovo06; @Poilblanc06] and numerical results for small systems.

In this work we employ analytic 