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)

BibTeX

@article{3daeffb83dff4baca5e7acb7d27a2c76,
title = "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 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.",
keywords = "cond-mat.stat-mech, hep-th, math-ph, math.MP, quant-ph",
author = "Robijn Vanhove and Laurens Lootens and {Van Damme}, Maarten and Ramona Wolf and Osborne, {Tobias J.} and Jutho Haegeman and Frank Verstraete",
note = "Funding Information: We are grateful for numerous helpful conversations, and correspondence, with Jacob Bridgeman, Cain Edie-Michell, Paul Fendley, J{\"u}rgen Fuchs, Ash Milsted, Christoph Schweigert, and Sukhwinder Singh. R. V. and L. L. are supported by a Fellowship from the Research Foundation Flanders (FWO). R. W. is supported by the Swiss National Science Foundation via the National Center for Competence in Research Quantum Science and Technology (NCCR QSIT) and the NCCR SwissMAP—The Mathematics of Physics. This work has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program [Grant Agreements No. 647905 (QUTE) and No. 715861 (ERQUAF)], and from the Research Foundation Flanders via Grant No. GOE1520N. Support by the DFG through SFB 1227 (DQ-mat), Quantum Valley Lower Saxony, and funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany{\textquoteright}s Excellence Strategy EXC-2123 QuantumFrontiers 390837967 are also acknowledged.",
year = "2022",
month = jun,
day = "10",
doi = "10.48550/arXiv.2110.03532",
language = "English",
volume = "128",
journal = "Physical review letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "23",
}