Symmetry fractionalization in the gauge mean-field theory of quantum spin ice

Abstract

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 $\pi$-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 $\pi /2$- and $3\pi /2$-fluxes of the emergent gauge field threading the hexagonal plaquettes of the pyrochlore lattice. We finally discuss 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.

12+10 pages, 4+1 figures

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• Spectroscopic signatures of fractionalization in octupolar quantum spin ice
• Emergent photons and fractionalized excitations in a quantum spin liquid
• A pseudofermion functional renormalization group study of dipolar-octupolar pyrochlore magnets
• Finite Temperature Dynamics in 0-Flux and $\pi$-Flux Quantum Spin Ice: Self-Consistent Exclusive Boson Approach
• Classification of symmetry-enriched topological quantum spin liquids
• Dipolar-octupolar correlations and hierarchy of exchange interactions in Ce${}_2$Hf${}_2$O${}_7$
• Signatures of spinon dynamics and phase structure of dipolar-octupolar quantum spin ices in two-dimensional coherent spectroscopy
• Vison crystal in quantum spin ice on the breathing pyrochlore lattice
• Chiral spin liquid phase in an optical lattice at mean-field level
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• Inelastic neutron scattering on Ce pyrochlores: Signatures of electric monopoles
• Pinch-line spin liquids as layered Coulomb phases and applications to cubic models
• Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints
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• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice