Critical Lattice Model for a Haagerup Conformal Field Theory
Abstract
We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the Haagerup fusion category 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 (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.
 Publication:

Physical Review Letters
 Pub Date:
 June 2022
 DOI:
 10.1103/PhysRevLett.128.231602
 arXiv:
 arXiv:2110.03532
 Bibcode:
 2022PhRvL.128w1602V
 Keywords:

 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 7 pages, 4 figures