Numerical evidence for a Haagerup conformal field theory

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.

4+1 pages, 7 figures; the authors are ordered alphabetically

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Cited by in corpus (32)

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• Bootstrapping Non-Invertible Symmetries
• Non-invertible Symmetries and Higher Representation Theory II
• Subsystem Non-Invertible Symmetry Operators and Defects
• A critical lattice model for a Haagerup conformal field theory
• Fusion Surface Models: 2+1d Lattice Models from Fusion 2-Categories
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• Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs
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• Noninvertible symmetries in the B model TFT
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• Virasoro and Kac-Moody algebra in generic tensor network representations of 2d critical lattice partition functions
• Les Houches Lecture Notes on Tensor Networks
• From gauging to duality in one-dimensional quantum lattice models
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