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Quantum Dimer Models (QDM) arise as low energy effective models forfrustrated magnets. Some of these models have proven successful in generating ascenario for exotic spin liquid phases with deconfined spinons. Doping, i.e.the introduction of mobile holes, has been considered within the QDM frameworkand partially studied. A fundamental issue is the possible existence of asuperconducting phase in such systems and its properties. For this purpose, thequestion of the statistics of the mobile holes (or "holons") shall be addressedfirst. Such issues are studied in details in this paper for generic doped QDMdefined on the most common two-dimensional lattices (square, triangular,honeycomb, kagome,...) and involving general resonant loops. We prove a general"statistical transmutation" symmetry of such doped QDM by using compositeoperators of dimers and holes. This exact transformation enables to defineduality equivalence classes (or families) of doped QDM, and provides theanalytic framework to analyze dynamical statistical transmutations. We discussvarious possible superconducting phases of the system. In particular, thepossibility of an exotic superconducting phase originating from thecondensation of (bosonic) charge-e holons is examined. A numerical evidence ofsuch a superconducting phase is presented in the case of the triangularlattice, by introducing a novel gauge-invariant holon Green's function. We alsomake the connection with a Bose-Hubbard model on the kagome lattice which givesrise, as an effective model in the limit of strong interactions, to a doped QDMon the triangular lattice.

Statistics of holes and nature of superfluid phases in Quantum dimer models