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Diagrammatics for Bose condensation in anyon theories

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arxiv 1310.6001 v2 pith:PXJ5KU52 submitted 2013-10-22 cond-mat.str-el hep-th

I.S. Eliëns , J.C. Romers , F.A. Bais This is my paper · ORCID
classification cond-mat.str-elhep-th
keywords phasevlcsdatatheoryanyonbosoniccalculatecondensates
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

Phase transitions in anyon models in (2+1)-dimensions can be driven by condensation of bosonic particle sectors. We study such condensates in a diagrammatic language and explicitly establish the relation between the states in the fusion spaces of the theory with the condensate, to the states in the parent theory using a new set of mathematical quantities called vertex lifting coefficients (VLCs). These allow one to calculate the full set of topological data ($S$-, $T$-, $R$- and $F$-matrices) in the condensed phase. We provide closed form expressions of the topological data in terms of the VLCs and provide a method by which one can calculate the VLCs for a wide class of bosonic condensates. We furthermore furnish a concrete recipe to lift arbitrary diagrams directly from the condensed phase to the original phase, such that they can be evaluated using the data of the original theory and a limited number of VLCs. Some representative examples are worked out in detail.

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Cited by 5 Pith papers

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

  1. Non-Invertible Anyon Condensation and Level-Rank Dualities

    hep-th 2023-12 unverdicted novelty 8.0 of 10

    New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.

  2. Proliferation transitions from a topological phase in $2+1$ dimensions

    cond-mat.str-el 2026-02 conditional novelty 7.0 of 10

    A general 2+1d transition theory out of a topological phase, driven by one Abelian anyon, is constructed and shown to depend on a single integer parameter, with p=0 giving gauging.

  3. Anyon Condensation In Symmetry-Enriched Topological Phases: $G$-Grading of Multifusion Categories

    cond-mat.str-el 2026-07 conditional novelty 6.0 of 10

    G-preserving anyon condensation in SET string-net models is equivalent to a compatible N-grading of the input multifusion category, which constructs the child SET input and works even with symmetry fractionalization.

  4. Landau-Ginzburg Paradigm of Topological Phases

    cond-mat.str-el 2025-06 conditional novelty 6.0 of 10

    A modified string-net model turns anyon condensation into a lattice version of the Higgs mechanism, putting some topological phase transitions into the Landau-Ginzburg symmetry-breaking framework.

  5. Information Loss in Generalized Symmetry Breaking

    quant-ph 2025-09 conditional novelty 4.0 of 10

    Anyon condensation is encoded as a conditional expectation between operator algebras, and the information it erases, measured by relative entropy, is claimed to be bounded by the log of the condensate's quantum dimension.

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