Recently, quantum dimer models, in which the system can tunnel between
different classical dimer configurations, have attracted a great deal of
interest as a paradigm for the study of exotic quantum phases. Much of this
excitement has centred on the claim that a certain class of quantum dimer
model, defined on a bipartite lattice, can support a quantum U(1)-liquid phase
with deconfined fractional excitations in three dimensions. These fractional
monomer excitations are quantum analogues of the magnetic monopoles found in
spin ice. In this article we use extensive quantum Monte Carlo simulations to
establish the ground-state phase diagram of the quantum dimer model on the
three-dimensional, bipartite, diamond lattice as a function of the ratio {\mu}
of the potential to kinetic energy terms in the Hamiltonian. We find that, for
{\mu}_c = 0.75 +/- 0.04, the model undergoes a first-order quantum phase
transition from an ordered "R-state" into an extended quantum U(1)-liquid
phase, which terminates in a quantum critical "RK point" for {\mu}=1. This
confirms the published field-theoretical scenario. We present detailed evidence
for the existence of the U(1)-liquid phase, and indirect evidence for the
existence of its photon and monopole excitations. We also explore some of the
technical ramifications of this analysis, benchmarking quantum Monte Carlo
against a variety of exact and perturbative results, comparing different
variational wave functions. The ergodicity of the quantum dimer model on a
diamond lattice is discussed in detail. These results complete and extend the
analysis previously published in [O. Sikora et al., Phys. Rev. Lett. 103,
247001 (2009)].Comment: 19 pages, 25 figures - we added a new figure and updated the
manuscrip
