A critical lattice model for a Haagerup conformal field theory

TL;DR

This paper constructs a two-dimensional critical lattice model based on the Haagerup fusion category, providing numerical evidence for a corresponding Haagerup conformal field theory with central charge 2, challenging existing construction conjectures.

Contribution

It introduces a novel lattice model derived from the Haagerup fusion category and demonstrates its conformal field theory properties through numerical analysis, offering a counterexample to standard CFT construction assumptions.

Findings

Numerical evidence supports a Haagerup CFT with c=2.

Spectra reveal topological sector separation.

Model obtained via orbifold from a larger lattice model.

Abstract

We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the \emph{Haagerup fusion category} $\mathcal{H}_3$ as input data. We present compelling numerical evidence in the form of finite entanglement scaling to support a Haagerup conformal field theory (CFT) with central charge $c=2$. Generalized twisted CFT spectra are numerically obtained through exact diagonalization of the transfer matrix and the conformal towers are separated in the spectra through their identification with the topological sectors. It is further argued that our model can be obtained through an orbifold procedure from a larger lattice model with input $Z(\mathcal{H}_3)$, which is the simplest modular tensor category that does not admit an algebraic construction. This provides a counterexample for the conjecture that all rational CFT can be constructed from standard methods.