Fractionalizing glide reflections in two-dimensional Z2 topologically ordered phases

TL;DR

This paper investigates how glide reflection symmetries in two-dimensional Z2 topologically ordered phases can be fractionalized, revealing new symmetry properties of topological excitations in non-symmorphic crystals.

Contribution

It generalizes the classification of gauge theories to include glide reflection symmetry, demonstrating how fractional quantum numbers can be detected numerically in specific models.

Findings

Fractionalized glide reflection quantum numbers identified.

Numerical detection methods for symmetry fractionalization developed.

Microscopic model exemplifies theoretical predictions.

Abstract

We study the fractionalization of space group symmetries in two-dimensional topologically ordered phases. Specifically, we focus on Z2-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 non-symmorphic 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.