Excitation basis for (3+1)d topological phases

Abstract

We consider an exactly solvable model in 3+1 dimensions, based on a finite group, which is a natural generalization of Kitaev's quantum double model. The corresponding lattice Hamiltonian yields excitations located at torus-boundaries. By cutting open the three-torus, we obtain a manifold bounded by two tori which supports states satisfying a higher-dimensional version of Ocneanu's tube algebra. This defines an algebraic structure extending the Drinfel'd double. Its irreducible representations, labeled by two fluxes and one charge, characterize the torus-excitations. The tensor product of such representations is introduced in order to construct a basis for (3+1)d gauge models which relies upon the fusion of the defect excitations. This basis is defined on manifolds of the form $\Sigma \times {\mathbb{S}}_1$, with $\Sigma$ a two-dimensional Riemann surface. As such, our construction is closely related to dimensional reduction from (3+1)d to (2+1)d topological orders.

33 pages; v2 references added; v3 minor changes

References in corpus (6)

• A classification of symmetry enriched topological phases with exactly solvable models
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• Dimensional Reduction and Topological Invariants of Symmetry-Protected Topological Phases
• Twisted Quantum Double Model of Topological Orders with Boundaries

Cited by in corpus (14)

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• Tube algebras, excitations statistics and compactification in gauge models of topological phases
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• Non-Abelian Hybrid Fracton Orders
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
• On 2-form gauge models of topological phases
• Entanglement entropy of (3+1)D topological orders with excitations
• Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
• Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders
• Excitations in strict 2-group higher gauge models of topological phases
• On tensor network representations of the (3+1)d toric code
• Towards a dual spin network basis for (3+1)d lattice gauge theories and topological phases
• Crossing with the circle in Dijkgraaf-Witten theory and applications to topological phases of matter