Theory of oblique topological insulators

Abstract

A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI phases are characterized by fractional $\Theta$-angles, long-range entanglement, and fractionalization. Starting from a simple family of ${\mathbb{Z}}_N$ lattice gauge theories due to Cardy and Rabinovici, we develop a class of FTI phases based on the physical mechanism of oblique confinement and the modern language of generalized global symmetries. We dub these phases oblique topological insulators. Oblique TIs arise when dyons -- bound states of electric charges and monopoles -- condense, leading to FTI phases characterized by topological order, emergent one-form symmetries, and gapped boundary states not realizable in 2+1-D alone. Based on the lattice gauge theory, we present continuum topological quantum field theories (TQFTs) for oblique TI phases involving fluctuating one-form and two-form gauge fields. We show explicitly that these TQFTs capture both the generalized global symmetries and topological orders seen in the lattice gauge theory. We also demonstrate that these theories exhibit a universal "generalized magnetoelectric effect" in the presence of two-form background gauge fields. Moreover, we characterize the possible boundary topological orders of oblique TIs, finding a new set of boundary states not studied previously for these kinds of TQFTs.

arXiv comment67 pages, 4 figures, 5 appendices. v2: new appendix, added references, and minor changes. v3: light revisions, additional discussion in Section 6 and Appendix E, and updated acknowledgements and references

References in corpus (49)

• Topological Insulators in Three Dimensions
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Generalized Global Symmetries
• Symmetry protected topological orders and the group cohomology of their symmetry group
• S-Duality of Boundary Conditions In N=4 Super Yang-Mills Theory
• Symmetry Protected Topological phases of Quantum Matter
• Coupling a QFT to a TQFT and Duality
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Theta, Time Reversal, and Temperature
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Generalized Symmetries in Condensed Matter
• Topological phases with parafermions: theory and blueprints
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Fractional topological insulators in three dimensions
• Three-dimensional topological lattice models with surface anyons
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Correlated Topological Insulators and the Fractional Magnetoelectric Effect
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Duality between $(2+1)d$ Quantum Critical Points
• Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly
• Disorder Operators and their Descendants
• Discrete Theta Angles, Symmetries and Anomalies
• An Adventure in Topological Phase Transitions in 3 + 1-D: Non-abelian Deconfined Quantum Criticalities and a Possible Duality
• Modular Invariance, Self-Duality and The Phase Transition Between Quantum Hall Plateaus
• Exactly soluble models for fractional topological insulators in 2 and 3 dimensions
• Superfluids as Higher-form Anomalies
• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• Effective field theories for topological insulators by functional bosonization
• Fermion condensation and super pivotal categories
• Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
• Confining String with Topological Term
• Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry
• A gauge theory generalization of the fermion-doubling theorem
• $S$-duality of $u(1)$ gauge theory with $\theta =\pi$ on non-orientable manifolds: Applications to topological insulators and superconductors
• Models of three-dimensional fractional topological insulators
• Topological Quantum Field Theory for Abelian Topological Phases and Loop Braiding Statistics in $(3+1)$-Dimensions
• Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order
• Effective hydrodynamic field theory and condensation picture of topological insulators
• Topological aspects of $4$D Abelian lattice gauge theories with the $\theta$ parameter
• Loop Models, Modular Invariance, and Three Dimensional Bosonization
• Physics of Symmetry Protected Topological phases involving Higher Symmetries and their Applications
• Phase transitions in three-dimensional topological lattice models with surface anyons
• Walker-Wang models and axion electrodynamics
• Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory
• Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly

Cited by in corpus (12)

• Obstructions to Gapped Phases from Non-Invertible Symmetries
• A Noisy Approach to Intrinsically Mixed-State Topological Order
• Exact emergent higher-form symmetries in bosonic lattice models
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Generalized symmetries in singularity-free nonlinear $\sigma$ models and their disordered phases
• Fusion rules and shrinking rules of topological orders in five dimensions
• Diagrammatics, Pentagon Equations, and Hexagon Equations of Topological Orders with Loop- and Membrane-like Excitations
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Intertwined order of generalized global symmetries
• Fermion-Vortex Interactions in Axion Electrodynamics
• Generalized symmetry enriched criticality in (3+1)d