A derivation of braided $C^{\ast }$-tensor categories from gapped ground states satisfying the approximate Haag duality

Abstract

We derive braided $C^{\ast }$-tensor categories from gapped ground states on two-dimensional quantum spin systems satisfying some additional condition which we call the approximate Haag duality.

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• Classification of the anyon sectors of Kitaev's quantum double model
• The category of anyon sectors for non-abelian quantum double models
• The index of a pair of pure states and the interacting integer quantum Hall effect
• $C^{\ast }$-categorical prefactorization algebras for superselection sectors and topological order