Employing large-scale quantum Monte Carlo simulations, we reveal the full phase diagram of hard-core boson model on the pyrochlore lattice with fractional fillings, considering the boson hopping as well as repulsion between nearest neighbor sites. Due to the partial boson filling, the system is in a cluster Mott insulator (Coulomb liquid) phase with bosons localized inside the tetrahedral units of the pyrochlore lattice when the inter-site repulsion is dominant. We show that the full phase diagram contains three Coulomb liquid phases in the Mott regime at 1/4, 1/2 and 3/4 boson fillings, all of which are described by the emergent compact U (1) quantum electrodynamics (QED). Besides measuring the specific heat and entropy of the cluster Mott insulator phases, we further investigate the boson density-density correlation function and find it is consistent with the electric field correlation of the compact U (1) QED. Our results shed lights on magnetic properties of various pyrochlore systems as well as the charge physics of the cluster magnets.
Zi-Yang Meng (Institute of Physics, Chinese Academy of Sciences)