  We investigate the quantum dynamics of monopole-like excitations in quantum
square ice, as captured by the strongly anisotropic spin-1/2 XXZ model on the
checkerboard lattice. We obtain exact results for excitation dynamics in both
analytically solvable effective models and a fully interacting model of quantum
square ice on finite clusters. We find that the dispersive lower bound of the
dynamic response of freely propagating spinons is recovered in the dynamic
structure factor of the interacting system, yielding a marked fingerprint of
coherent spinon dispersion. Our results provide unbiased evidence for the
formation of coherent quasiparticles propagating freely in the correlated
"vacuum" of quantum square ice.
