Speaker
Description
The critical behaviour at a second-order phase transition is often described by a conformal field theory. The restrictions imposed by conformal symmetry give rise to a number of important theoretical techniques that have made these theories central to the understanding of critical phenomena. However, efforts to classify conformal field theories have run into the challenge of identifying lattice models that have a corresponding critical point. Here, we introduce an algorithm that we call a conformal field theory factory for methodically generating two-dimensional lattice models that would flow to conformal field theories in the infrared limit. We realise these lattice models by engineering the boundary conditions of three-dimensional topological orders described by string-net models. The critical points are induced by a commensurate condensation of non-commuting anyons. Our structured method generates an infinite family of critical lattice models, including previously unknown critical points. We recover known conformal field theories that preserve the Haagerup symmetries and identify three further candidate theories. The critical couplings of our models are precisely encoded in algebraic data associated with the string-net models, thereby establishing a scheme for discovering and potentially classifying conformal field theories.
Relevant references: arXiv:2506.05324.