Critical Lattice Model for a Haagerup Conformal Field Theory

authored by

Robijn Vanhove, Laurens Lootens, Maarten Van Damme, Ramona Wolf, Tobias J. Osborne, Jutho Haegeman, Frank Verstraete

Abstract

We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the Haagerup fusion category H3 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(H3), 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.

Organisation(s)

Nanostructures Section
Institute of Theoretical Physics
QuantumFrontiers
CRC 1227 Designed Quantum States of Matter (DQ-mat)

External Organisation(s)

Ghent University

Type

Article

Journal

Physical review letters

Volume

128

ISSN

0031-9007

Publication date

10.06.2022

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Physics and Astronomy(all)

Electronic version(s)

https://doi.org/10.48550/arXiv.2110.03532 (Access: Open)
https://doi.org/10.1103/PhysRevLett.128.231602 (Access: Closed)
https://biblio.ugent.be/publication/8759783 (Access: Open)