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Classification of Topological Defects in Abelian Topological States

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arxiv 1304.7579 v1 pith:NOJDJLWZ submitted 2013-04-29 cond-mat.str-el

Maissam Barkeshli , Chao-Ming Jian , Xiao-Liang Qi This is my paper · ORCID
classification cond-mat.str-el
keywords defectstopologicalclassificationabelianboundarydistinctextrinsicgeneric
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In this paper we propose the most general classification of point-like and line-like extrinsic topological defects in (2+1)-dimensional Abelian topological states. We first map generic extrinsic defects to boundary defects, and then provide a classification of the latter. Based on this classification, the most generic point defects can be understood as domain walls between topologically distinct boundary regions. We show that topologically distinct boundaries can themselves be classified by certain maximal subgroups of mutually bosonic quasiparticles, called Lagrangian subgroups. We study the topological properties of the point defects, including their quantum dimension, localized zero modes, and projective braiding statistics.

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Cited by 3 Pith papers

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  1. Higher Gauging and Non-invertible Condensation Defects

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    Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.

  2. Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy II -- Cutting through the boundary

    hep-th 2019-08 conditional novelty 6.0 of 10

    When an entanglement cut ends on a gapped boundary of a 2+1D topological phase, the topological entanglement entropy is controlled by the half-linking matrix, which replaces the modular S matrix used without boundaries.

  3. What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries

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    A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.

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