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Critical lattice model for a Haagerup conformal field theory

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Abstract
We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the Haagerup fusion category 7-13 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(7-13), 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.
Keywords
General Physics and Astronomy, ENTANGLEMENT, CONSTRUCTION, SUBFACTORS, SYMMETRY, ENTROPY

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MLA
Vanhove, Robijn, et al. “Critical Lattice Model for a Haagerup Conformal Field Theory.” PHYSICAL REVIEW LETTERS, vol. 128, no. 23, 2022, doi:10.1103/physrevlett.128.231602.
APA
Vanhove, R., Lootens, L., Van Damme, M., Wolf, R., Osborne, T. J., Haegeman, J., & Verstraete, F. (2022). Critical lattice model for a Haagerup conformal field theory. PHYSICAL REVIEW LETTERS, 128(23). https://doi.org/10.1103/physrevlett.128.231602
Chicago author-date
Vanhove, Robijn, Laurens Lootens, Maarten Van Damme, Ramona Wolf, Tobias J. Osborne, Jutho Haegeman, and Frank Verstraete. 2022. “Critical Lattice Model for a Haagerup Conformal Field Theory.” PHYSICAL REVIEW LETTERS 128 (23). https://doi.org/10.1103/physrevlett.128.231602.
Chicago author-date (all authors)
Vanhove, Robijn, Laurens Lootens, Maarten Van Damme, Ramona Wolf, Tobias J. Osborne, Jutho Haegeman, and Frank Verstraete. 2022. “Critical Lattice Model for a Haagerup Conformal Field Theory.” PHYSICAL REVIEW LETTERS 128 (23). doi:10.1103/physrevlett.128.231602.
Vancouver
1.
Vanhove R, Lootens L, Van Damme M, Wolf R, Osborne TJ, Haegeman J, et al. Critical lattice model for a Haagerup conformal field theory. PHYSICAL REVIEW LETTERS. 2022;128(23).
IEEE
[1]
R. Vanhove et al., “Critical lattice model for a Haagerup conformal field theory,” PHYSICAL REVIEW LETTERS, vol. 128, no. 23, 2022.
@article{8759783,
  abstract     = {{We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the Haagerup fusion category 7-13 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(7-13), 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.}},
  articleno    = {{231602}},
  author       = {{Vanhove, Robijn and Lootens, Laurens and Van Damme, Maarten and Wolf, Ramona and Osborne, Tobias J. and Haegeman, Jutho and Verstraete, Frank}},
  issn         = {{0031-9007}},
  journal      = {{PHYSICAL REVIEW LETTERS}},
  keywords     = {{General Physics and Astronomy,ENTANGLEMENT,CONSTRUCTION,SUBFACTORS,SYMMETRY,ENTROPY}},
  language     = {{eng}},
  number       = {{23}},
  pages        = {{6}},
  title        = {{Critical lattice model for a Haagerup conformal field theory}},
  url          = {{http://doi.org/10.1103/physrevlett.128.231602}},
  volume       = {{128}},
  year         = {{2022}},
}

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