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Theory of Twist Liquids: Gauging an Anyonic Symmetry

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arxiv 1503.06812 v2 pith:UVTHVJIW submitted 2015-03-23 cond-mat.str-el

Jeffrey C. Y. Teo , Taylor L. Hughes , Eduardo Fradkin This is my paper · ORCID
classification cond-mat.str-el
keywords gaugingstatetwistliquidstopologicalanyonsdefectsnon-abelian
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Topological phases in (2+1)-dimensions are frequently equipped with global symmetries, like conjugation, bilayer or electric-magnetic duality, that relabel anyons without affecting the topological structures. Twist defects are static point-like objects that permute the labels of orbiting anyons. Gauging these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases referred as twist liquids, which are generically non-Abelian. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. We explicitly demonstrate the gauging of the $\mathbb{Z}_2$-symmetric toric code, $SO(2N)_1$ and $SU(3)_1$ state as well as the $S_3$-symmetric $SO(8)_1$ state and a non-Abelian chiral state we call the "4-Potts" state.

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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. Non-Invertible Symmetries in 6d from Green-Schwarz Automorphisms

    hep-th 2024-11 conditional novelty 7.0 of 10

    Non-invertible S3-ality defects are constructed in the 6d (2,0) so(8) SCFT, with fusion rules computed by half-space gauging and SymTFT.

  2. SymSETs and self-dualities under gauging non-invertible symmetries

    hep-th 2025-01 conditional novelty 6.0 of 10

    A new SymSET-based construction shows that changing symmetry fractionalization classes can change fusion rules of self-duality defects under non-invertible gauging, yielding new fusion categories such as Rep D16 and Rep SD16.

  3. ICTP Lectures on (Non-)Invertible Generalized Symmetries

    hep-th 2023-05 accept novelty 2.0 of 10

    Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.

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