  We demonstrate that the insulating one-band Hubbard model on the pyrochlore
lattice contains, for realistic parameters, an extended quantum spin-liquid
phase. This is a three-dimensional spin liquid formed from a highly degenerate
manifold of dimer-based states, which is a subset of the classical dimer
coverings obeying the ice rules. It possesses spinon excitations, which are
both massive and deconfined, and on doping it exhibits spin-charge separation.
We discuss the realization of this state in effective S = 1/2 pyrochlore
materials with and without spin-orbit coupling.
