Dirac's "magnetic monopoles" in pyrochlore ice U(1) spin liquids: Spectrum and classification

We study the U(1) quantum spin liquid on the pyrochlore spin ice systems. For the non-Kramers doublets such as Pr3+ and Tb3+, we point out that the inelastic neutron scattering result not only detects the low-energy gauge photon, but also contains the continuum of the "magnetic monopole" excitations. Unlike spinons, these "magnetic monopoles" are purely of quantum origin and have no classical analog. We further point out that the "magnetic monopole" experiences a background dual "pi" flux due to the spin-1/2 nature of the local moment when the "monopole" hops on the dual diamond lattice. We then predict that the "monopole" continuum has an enhanced spectral periodicity with a folded Brillouin zone. This prediction can be examined among the existing data on non-Kramers doublet spin liquid candidate materials like Pr2TM2O7 and Tb2TM2O7 (with TM = transition metal). The application to the Kramers doublet systems and numerical simulation is further discussed. Finally, we present a general classification of distinct symmetry enriched U(1) quantum spin liquids based on the translation symmetry fractionalization patterns of "monopoles" and "spinons."