Numerical evidence of quantum melting of spin ice: quantum-classical crossover

Unbiased quantum Monte-Carlo simulations are performed on the simplest case of the quantum spin ice model, namely, the nearest-neighbor spin-$\frac{1}{2}$ XXZ model on the pyrochlore lattice with an antiferromagnetic longitudinal and a weak ferromagnetic transverse exchange couplings, $J$ and $J_\perp$. On cooling across $T_{\mathrm{CSI}}\sim0.2J$, the specific heat shows a broad peak associated with a crossover to a classical Coulomb liquid regime characterized by a remnant of the pinch-point singularity in longitudinal spin correlations as well as the Pauling ice entropy for $|J_\perp|\ll J$, as in classical spin ice. On further cooling, the entropy restarts gradually decaying to zero for $J_\perp>J_{\perp c}\sim-0.104J$, as expected for bosonic quantum Coulomb liquids. With negatively increasing $J_\perp$ across $J_{\perp c}$, a first-order transition occurs at a nonzero temperature from the quantum Coulomb liquid to an XY ferromagnet. Relevance to magnetic rare-earth pyrochlore oxides is discussed.