A critical lattice model for a Haagerup conformal field theory

• URL: http://arxiv.org/abs/2110.03532v1
• Date: Thu, 7 Oct 2021 14:57:52 GMT
• Title: A critical lattice model for a Haagerup conformal field theory
• Authors: Robijn Vanhove and Laurens Lootens and Maarten Van Damme and Ramona Wolf and Tobias Osborne and Jutho Haegeman and Frank Verstraete
• Abstract summary: We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions. We present compelling numerical evidence in the form of finite entanglement scaling to support a Haagerup conformal field theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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