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We study the U(1) quantum spin liquid on the pyrochlore spin ice systems. Forthe non-Kramers doublets such as Pr$^{3+}$ and Tb$^{3+}$, we point out that theinelastic neutron scattering not only detects the low-energy gauge photon, butalso contains the continuum of the "magnetic monopole" excitations. Unlike thespinons, these "magnetic monopoles" are purely of quantum origin and have noclassical analogue. We further point out that the "magnetic monopole"experiences a background dual "$\pi$" flux due to the spin-1/2 nature of thelocal moment when the "monopole" hops on the dual diamond lattice. We thenpredict that the "monopole" continuum has an enhanced spectral periodicity.This prediction can be examined among the existing data on the non-Kramersdoublet spin liquid candidate materials like Pr$_2$TM$_2$O$_7$ andTb$_2$TM$_2$O$_7$ (with TM = "transition metal"). The application to theKramers doublet systems and numerical simulation is further discussed. Finally,we present a general classification of distinct symmetry enriched U(1) quantumspin liquids based on the translation symmetry fractionalization patterns of"monopoles" and "spinons".

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