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arXiv · 2503.15611

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

Alex Bols·Mahdie Hamdan·Pieter Naaijkens·Siddharth Vadnerkar
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Abstract

We study Kitaev's quantum double model for arbitrary finite gauge group in infinite volume, using an operator-algebraic approach. The quantum double model hosts anyonic excitations which can be identified with equivalence classes of `localized and transportable endomorphisms', which produce anyonic excitations from the ground state. Following the Doplicher--Haag--Roberts (DHR) sector theory from AQFT, we organize these endomorphisms into a braided monoidal category capturing the fusion and braiding properties of the anyons. We show that this category is equivalent to $\mathrm{Rep}_f \mathcal{D}(G)$, the representation category of the quantum double of $G$. This establishes for the first time the full DHR structure for a class of 2d quantum lattice models with non-abelian anyons.

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Alex Bols, Mahdie Hamdan, Pieter Naaijkens, Siddharth Vadnerkar. 2025-03-19. The category of anyon sectors for non-abelian quantum double models. https://doi.org/10.1007/s00220-025-05492-2

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