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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 usingseveral local and global observables. In addition, we analyze imaginary-timecorrelation functions to determine ground state energies as well as gaps to thefirst excited states. This leads in particular to a confirmation that theintermediary so-called plaquette phase is gapped -- a point which waspreviously advocated with general arguments and some data for an orderparameter, but required a more direct proof. On the technical side, we describean efficient world-line quantum Monte Carlo algorithm with improved clusterupdates that increase acceptance probabilities by taking account of potentialterms of the Hamiltonian during the cluster construction. The Monte Carlosimulations are supplemented with variational computations.

Phase diagram of the hexagonal lattice quantum dimer model: Order parameters, ground-state energy, and gaps