Quantum Dimer Models (QDM) arise as low energy effective models for frustrated magnets. Some of these models have proven successful in generating a scenario for exotic spin liquid phases with deconfined spinons. Doping, i.e. the introduction of mobil
e holes, has been considered within the QDM framework and partially studied. A fundamental issue is the possible existence of a superconducting phase in such systems and its properties. For this purpose, the question of the statistics of the mobile holes (or holons) shall be addressed first. Such issues are studied in details in this paper for generic doped QDM defined 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 composite operators of dimers and holes. This exact transformation enables to define duality equivalence classes (or families) of doped QDM, and provides the analytic framework to analyze dynamical statistical transmutations. We discuss various possible superconducting phases of the system. In particular, the possibility of an exotic superconducting phase originating from the condensation of (bosonic) charge-e holons is examined. A numerical evidence of such a superconducting phase is presented in the case of the triangular lattice, by introducing a novel gauge-invariant holon Greens function. We also make the connection with a Bose-Hubbard model on the kagome lattice which gives rise, as an effective model in the limit of strong interactions, to a doped QDM on the triangular lattice.
We argue that the spin-wave breakdown in the Heisenberg kagome antiferromagnet signals an instability of the ground state and leads, through an emergent local constraint, to a quantum dynamics described by a gauge theory similar to that of chromodyna
mics. For integer spins, we show that the quantum fluctuations of the gauge modes select the sqrt(3)xsqrt(3) Neel state with an on-site moment renormalized by color resonances. We find non-magnetic low-energy excitations that may be responsible for a deconfinement transition at experimentally accessible temperatures which we estimate.
Bosonic and fermionic Hubbard models on the checkerboard lattice are studied numerically for infinite on-site repulsion. At particle density n=1/4 and strong nearest-neighbor repulsion, insulating Valence Bond Crystals (VBC) of resonating particle pa
irs are stabilized. Their melting into superfluid/metallic phases under increasing hopping is investigated at T=0K. More specifically, we identify a novel and unconventional commensurate VBC supersolid region, precursor to the melting of the bosonic crystal. Hardcore bosons (spins) are compared to fermions (electrons), as well as positive to negative (frustrating) hoppings.
