Numerical Evidence for a Haagerup Conformal Field Theory

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 ???2. Fusion categories generalize the concept of finite group symmetries to noninvertible symmetry operations, and the Haagerup fusion category is the simplest one which comes from neither finite groups nor affine Lie algebras. As such, ours is the first example of conformal field theories which have truly exotic generalized symmetries. Basically the same result was independently obtained in the preceding Letter [Phys. Rev. Lett. 128, 231602 (2022)].

Automated summary

We numerically studied an anyon chain based on the Haagerup fusion category and found evidence that it leads to a conformal field theory in the long-distance limit, with a central charge of ???2. This is the first example of a conformal field theory with truly exotic generalized symmetries.