Symmetry fractionalization in quantum spin ice

Symmetry fractionalization is a ubiquitous feature of topologically ordered states that can be used to classify different symmetry-enriched topological phases and reveal some of their unique experimental signatures. Despite its vast popularity, there is currently no available framework to study symmetry fractionalization of quantum spin ice (QSI) — a U(1) quantum spin liquid (QSL) on the pyrochlore lattice supporting emergent photons — within the most widely used theoretical framework to describe it, gauge mean-field theory (GMFT). In this work, we provide an extension of GMFT that allows for the classification of space-time symmetry fractionalization. The construction classifies all GMFT Ansätze that yield physical wavefunctions invariant under given symmetries and a specific low-energy gauge structure. As an application of the framework, we first show that the only two Ansätze with emergent U(1) gauge fields that respect all space-group symmetries are the well-known 0- and π-flux states. We then showcase how the framework may describe QSLs beyond the currently known ones by classifying chiral U(1) QSI. We find two new states described by π/2- and 3π/2-fluxes of the emergent gauge field threading the hexagonal plaquettes of the pyrochlore lattice. We then examine how the different ways translation symmetries fractionalize for all these states lead to unique experimentally relevant signatures and compute their respective inelastic neutron scattering cross-section to illustrate the argument. We end by discussing how our framework can be extended to study Z₂ QSLs born out of spinon pairs condensation, QSI on the breathing pyrochlore lattice where inversion symmetry is broken, and the dipolar-octupolar case relevant for Ce₂Zr₂O₇.