Fractionalizing glide reflections in two-dimensional Z(2) topologically ordered phases

Abstract

We study the fractionalization of space group symmetries in two-dimensional topologically ordered phases. Specifically, we focus on Z(2)-fractionalized phases in two dimensions whose deconfined topological excitations transform trivially under translational symmetries but projectively under glide reflections, whose quantum numbers are hence fractionalized. We accomplish this by generalizing the dichotomy between even and odd gauge theories to incorporate additional symmetries inherent to nonsymmorphic crystals. We show that the resulting fractionalization of point group quantum numbers can be detected in numerical studies of ground state wave functions. We illustrate these ideas using a microscopic model of a system of bosons at integer unit cell filling on a lattice with space group p4g that can be mapped to a half-magnetization plateau for an S = 1/2 spin system on the Shastry-Sutherland lattice.