Classification of the anyon sectors of Kitaev's quantum double model

Abstract

We give a complete classification of the anyon sectors of Kitaev's quantum double model on the infinite triangular lattice and for finite gauge group $G$, including the non-abelian case. As conjectured, the anyon sectors of the model correspond precisely to equivalence classes of irreducible representations of the quantum double algebra of $G$.

arXiv commentpublished version. 62 pages, 14 figures

References in corpus (19)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Anyons in an exactly solved model and beyond
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• String-net condensation: A physical mechanism for topological phases
• Entanglement spectrum of topological insulators and superconductors
• A statistical mechanics view on Kitaev's proposal for quantum memories
• Microscopic definitions of anyon data
• Localized endomorphisms in Kitaev's toric code on the plane
• Quantum Chains of Hopf Algebras with Quantum Double Cosymmetry
• Haag duality for Kitaev's quantum double model for abelian groups
• Haag duality and the distal split property for cones in the toric code
• A derivation of braided $C^{\ast }$-tensor categories from gapped ground states satisfying the approximate Haag duality
• The complete set of infinite volume ground states for Kitaev's abelian quantum double models
• On the stability of charges in infinite quantum spin systems
• Kitaev's quantum double model from a local quantum physics point of view
• Kosaki-Longo index and classification of charges in 2D quantum spin models
• On the Quantum Symmetry of the Chiral Ising Model
• The Quantum Symmetry of Rational Field Theories

Cited by in corpus (1)

• The category of anyon sectors for non-abelian quantum double models