Extended Coulomb Liquid of Paired Hardcore Boson Model on a Pyrochlore Lattice

There is a growing interest in the U(1) Coulomb liquid in both quantum materials in pyrochlore ice and cluster Mott insulators and cold atom systems. We explore a paired hardcore boson model on a pyrochlore lattice. This model is equivalent to the XYZ spin model that was proposed for rare-earth pyrochlores with ''dipole-octupole'' doublets. Since this model has no sign problem for quantum Monte Carlo(QMC) simulations in a large parameter regime, we carry out both analytical and QMC calculations. We find that the U(1) Coulomb liquid is quite stable and spans a rather large portion of the phase diagram with boson pairing. Moreover, we numerically find thermodynamic evidence that the boson pairing could induce a possible Z₂ liquid in the vicinity of the phase boundary between Coulomb liquid and Z₂ symmetry-broken phase. Besides the materials' relevance with quantum spin ice, we point to quantum simulation with cold atoms on optical lattices.