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Abstract

Recently, quantum dimer models have attracted a great deal of interest as a paradigm for the study of exotic quantum phases. Much of this excitement has centered on the claim that a certain class of quantum dimer model can support a quantum U(1)-liquid phase with deconfined fractional excitations in three dimensions. These fractional monomer excitations are quantum analogs of the magnetic monopoles found in spin ice. In this paper, we use extensive quantum Monte Carlo simulations to establish the ground-state phase diagram of the quantum dimer model on the three-dimensional 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 +/- 0.02, 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 Rokhsar-Kivelson (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. Simulations are benchmarked against a variety of exact and perturbative results, and a comparison is made of different variational wave functions. We also explore the ergodicity of the quantum dimer model on a diamond lattice within a given flux sector, identifying a new conserved quantity related to transition graphs of dimer configurations. These results complete and extend the previous analysis of O. Sikora et al. [Phys. Rev. Lett. 103, 247001 (2009)].