  The phase diagram of the quantum dimer model on the hexagonal (honeycomb)
lattice is computed numerically, extending on earlier work by Moessner, Sondhi,
and Chandra. The different ground state phases are studied in detail using
several local and global observables. In addition, we analyze imaginary-time
correlation functions to determine ground state energies as well as gaps to the
first excited states. This leads in particular to a confirmation that the
intermediary so-called plaquette phase is gapped -- a point which was
previously advocated with general arguments and some data for an order
parameter, but required a more direct proof. On the technical side, we describe
an efficient world-line quantum Monte Carlo algorithm with improved cluster
updates that increase acceptance probabilities by taking account of potential
terms of the Hamiltonian during the cluster construction. The Monte Carlo
simulations are supplemented with variational computations.
