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<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textbf{Rep}_f {{\mathcal {D}}}(G)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="bold">Rep</mi> <mi>f</mi> </msub> <mi mathvariant="script">D</mi> <mrow> <mo stretchy="false">(</mo> <mi>G</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, the representation category of the quantum double of <i>G</i>. This establishes for the first time the full DHR structure for a class of 2d quantum lattice models with non-abelian anyons.</p>

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The Category of Anyon Sectors for Non-Abelian Quantum Double Models

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月5日

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  • Alex Bols,
  • Mahdie Hamdan,
  • Pieter Naaijkens,
  • Siddharth Vadnerkar

摘要

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 \(\textbf{Rep}_f {{\mathcal {D}}}(G)\) Rep f 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.