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Anyonic Entanglement and Topological Entanglement Entropy

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arxiv 1706.09420 v2 pith:AYKBHVFY submitted 2017-06-28 quant-ph cond-mat.str-el

Parsa Bonderson , Christina Knapp , Kaushal Patel This is my paper · ORCID
classification quant-phcond-mat.str-el
keywords entanglementanyonicentropysystemstopologicalgeneralnonlocalphases
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We study the properties of entanglement in two-dimensional topologically ordered phases of matter. Such phases support anyons, quasiparticles with exotic exchange statistics. The emergent nonlocal state spaces of anyonic systems admit a particular form of entanglement that does not exist in conventional quantum mechanical systems. We study this entanglement by adapting standard notions of entropy to anyonic systems. We use the algebraic theory of anyon models (modular tensor categories) to illustrate the nonlocal entanglement structure of anyonic systems. Using this formalism, we present a general method of deriving the universal topological contributions to the entanglement entropy for general system configurations of a topological phase, including surfaces of arbitrary genus, punctures, and quasiparticle content. We analyze a number of examples in detail. Our results recover and extend prior results for anyonic entanglement and the topological entanglement entropy.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes

    hep-th 2025-05 unverdicted novelty 6.0 of 10

    Minimal edge modes compatible with Chern-Simons topological invariance are proposed as quantum group particles, yielding a factorization of 3d gravity state space that matches proposals linking Bekenstein-Hawking entr...

  2. Modular evolutions and causality in two-dimensional conformal field theory

    hep-th 2025-01 accept novelty 6.0 of 10

    Modular flows preserve causal spacetime ordering inside causal diamonds, but a bilocal modular Hamiltonian can violate local commutativity at spacelike distances.

  3. Entanglement and geometric transitions in topological string theory

    hep-th 2026-07 conditional novelty 5.5 of 10

    Open-string anyonic entanglement on entanglement branes equals gravitational replica entropy of the dual closed-string Calabi–Yau via geometric transitions in the A-model TQFT.

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