  We prove a "statistical transmutation" symmetry of doped quantum dimer models
on the square, triangular and kagome lattices: the energy spectrum is invariant
under a simultaneous change of statistics (i.e. bosonic into fermionic or
vice-versa) of the holes and of the signs of all the dimer resonance loops.
This exact transformation enables to define duality equivalence between doped
quantum dimer Hamiltonians, and provides the analytic framework to analyze
dynamical statistical transmutations. We investigate numerically the doping of
the triangular quantum dimer model, with special focus on the topological Z2
dimer liquid. Doping leads to four (instead of two for the square lattice)
inequivalent families of Hamiltonians. Competition between phase separation,
superfluidity, supersolidity and fermionic phases is investigated in the four
families.

Strongly Correlated Electrons