  We study the mechanism of loop condensation in the quantum dimer model on the
triangular lattice. The triangular lattice quantum dimer model displays a
topologically ordered quantum liquid phase in addition to conventionally
ordered phases with broken symmetry. In the context of systems with extended
loop-like degrees of freedom, the formation of such topological order can be
described in terms of loop condensation. Using Monte Carlo calculations with
local and directed-loop updates, we compute geometric properties of the
transition graph loop distributions of several triangular lattice quantum dimer
wavefunctions that display dimer-liquid to dimer-crystal transitions and
characterize these in terms of loop condensation.
