Three-dimensional anomalous twisted gauge theories with global symmetry: Implications for quantum spin liquids

Abstract

Topological spin liquids can be described by topological gauge theories with global symmetry. Due to the presence of both nontrivial bulk deconfined gauge fluxes and global symmetry, topological spin liquids are examples of the so-called "Symmetry Enriched Topological phases" (SET). In this paper, we find that, in some twisted versions of topological gauge theories (with discrete Abelian gauge group $G_g$), implementing a global symmetry (denoted by $G_s$) is anomalous although symmetry charge carried by topological point-like excitations is normally fractionalized and classified by the second cohomology group. To demonstrate the anomaly, we fully gauge the global symmetry, rendering a new gauge theory that is not gauge invariant. Therefore, the SET order of the ground state is anomalous, which cannot exist in 3D system alone. Such anomalous state construction generalizes the "2D surface topological order" to 3D. A concrete example with $G_g={\mathbb{Z}}_2\times {\mathbb{Z}}_4$ and $G_s={\mathbb{Z}}_2$ is calculated.

4 pages

References in corpus (17)

• Hyper-honeycomb iridate $\beta$-Li2IrO3 as a platform for Kitaev magnetism
• Recent progress on correlated electron systems with strong spin-orbit coupling
• Non-coplanar and counter-rotating incommensurate magnetic order stabilized by Kitaev interactions in $\gamma$-Li2IrO3
• Unconventional magnetic order on the hyperhoneycomb Kitaev lattice in $\beta$-Li2IrO3: full solution via magnetic resonant x-ray diffraction
• Anomalies of discrete symmetries in three dimensions and group cohomology
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Symmetry Fractionalization in Two Dimensional Topological Phases
• Wilson operator algebras and ground states for coupled BF theories
• Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry
• Field Theories for Gauged Symmetry Protected Topological Phases: Abelian Gauge Theories with non-Abelian Quasiparticles
• Entanglement entropy of (3+1)D topological orders with excitations
• Symmetry Enrichment in Three-Dimensional Topological Phases
• Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order
• Realizing anomalous anyonic symmetries at the surfaces of 3d gauge theories
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Symmetry fractionalization and anomaly detection in three-dimensional topological phases
• Symmetry Fractionalization in Three-Dimensional ${\mathbb{Z}}_2$ Topological Order and Fermionic Symmetry-Protected Phases

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