Extended Coulomb liquid of paired hardcore boson model on a pyrochlore lattice

TL;DR

This paper investigates a paired hardcore boson model on a pyrochlore lattice, demonstrating the stability of a $U(1)$ Coulomb liquid phase and suggesting the emergence of a $bZ_2$ liquid near phase boundaries, with implications for quantum materials and cold atom systems.

Contribution

It provides the first combined analytical and quantum Monte Carlo study of a paired hardcore boson model on a pyrochlore lattice, revealing a stable Coulomb liquid and potential $bZ_2$ phase.

Findings

$U(1)$ Coulomb liquid is stable over a large phase space.

Boson pairing may induce a $bZ_2$ liquid near phase boundaries.

Model is relevant for quantum spin ice and cold atom quantum simulation.

Abstract

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 $\mathbb{Z}_2$ liquid in the vicinity of the phase boundary between Coulomb liquid and $\mathbb{Z}_2$ symmetry-broken phase. Besides the materials' relevance with quantum spin ice, we point to quantum simulation with cold atoms on optical lattices.