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Numerical evidence for a Haagerup conformal field theory

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arxiv 2110.03008 v1 pith:SPOYXZH5 submitted 2021-10-06 cond-mat.stat-mech cond-mat.str-elhep-thmath.OAmath.QA

Tzu-Chen Huang , Ying-Hsuan Lin , Kantaro Ohmori , Yuji Tachikawa , Masaki Tezuka This is my paper
classification cond-mat.stat-mechcond-mat.str-elhep-thmath.OAmath.QA
keywords conformalfieldfusionhaagerupcategoryevidencefinitesymmetries
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abstract

We numerically study an anyon chain based on the Haagerup fusion category, and find evidence that it leads in the long-distance limit to a conformal field theory whose central charge is $\sim 2$. Fusion categories generalize the concept of finite group symmetries to non-invertible symmetry operations, and the Haagerup fusion category is the simplest one which comes neither from finite groups nor affine Lie algebras. As such, ours is the first example of conformal field theories which have truly exotic generalized symmetries.

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Cited by 4 Pith papers

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

  1. Non-Local Conserved Currents and Continuous Non-Invertible Symmetries

    hep-th 2025-07 conditional novelty 7.0 of 10

    Non-local conserved currents attached to topological lines generate continuous non-invertible symmetries in 1+1d CFTs, with new examples in SU(2)_k WZW and minimal model products.

  2. A 2D-CFT Factory: Critical Lattice Models from Competing Anyon Condensation Processes in SymTO/SymTFT

    cond-mat.str-el 2025-06 conditional novelty 7.0 of 10

    Competing anyon condensates in string-net models generate critical lattice models, including new Haagerup-symmetric CFT candidates with central charges near 1.3, 1.8 and 2.5.

  3. Irrational CFTs from coupled anyon chains with non-invertible symmetries?

    hep-th 2025-07 conditional novelty 6.0 of 10

    DMRG evidence from three coupled Fibonacci anyon chains points to a conformal phase with c=2.10±0.03, proposed as a candidate irrational CFT, though small system sizes leave a weakly first-order alternative open.

  4. Les Houches Lecture Notes on Tensor Networks

    cond-mat.str-el 2025-12 unverdicted novelty 2.0 of 10

    A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.

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