We report low-temperature thermal conductivity $kappa$ of pyrochlore Yb$_2$Ti$_2$O$_7$, which contains frustrated spin-ice correlations with significant quantum fluctuations. In the disordered spin-liquid regime, $kappa(H)$ exhibits a nonmonotonic magnetic field dependence, which is well explained by the strong spin-phonon scattering and quantum monopole excitations. We show that the excitation energy of quantum monopoles is strongly suppressed from that of dispersionless classical monopoles. Moreover, in stark contrast to the diffusive classical monopoles, the quantum monopoles have a very long mean free path. We infer that the quantum monopole is a novel heavy particle, presumably boson, which is highly mobile in a three-dimensional spin liquid.
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