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We study the fractionalization of space group symmetries in two-dimensionaltopologically ordered phases. Specifically, we focus on Z2-fractionalizedphases in two dimensions whose deconfined topological excitations transformtrivially under translational symmetries, but projectively under glidereflections, whose quantum numbers are hence fractionalized. We accomplish thisby generalizing the dichotomy between even and odd gauge theories toincorporate additional symmetries inherent to non-symmorphic crystals. We showthat the resulting fractionalization of point group quantum numbers can bedetected in numerical studies of ground state wave functions. We illustratethese ideas using a microscopic model of a system of bosons at integer unitcell filling on a lattice with space group p4g, that can be mapped to ahalf-magnetization plateau for an S =1/2 spin system on the Shastry-Sutherlandlattice.

Fractionalizing glide reflections in two-dimensional Z2 topologically ordered phases