Critical Lattice Model for a Haagerup Conformal Field Theory.

@article{Vanhove2022CriticalLM,
  title={Critical Lattice Model for a Haagerup Conformal Field Theory.},
  author={Robijn Vanhove and Laurens Lootens and Martin Van Damme and Ramona Wolf and Tobias J. Osborne and Jutho Haegeman and F. Verstraete},
  journal={Physical review letters},
  year={2022},
  volume={128 23},
  pages={
          231602
        }
}
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… 

Figures and Tables from this paper

Virasoro and Kac-Moody algebra in generic tensor network representations of 2d critical lattice partition functions
In this paper, we propose a general implementation of the Virasoro generators and Kac–Moody currents in generic tensor network representations of 2-dimensional critical lattice models. Our proposal
Anyon braiding and the renormalization group
A braiding operation defines a real-space renormalization group for anyonic chains. The resulting renormalization group flow can be used to define a quantum scaling limit by operator-algebraic
Anyonic Chains -- $\alpha$-Induction -- CFT -- Defects -- Subfactors
Given a unitary fusion category, one can define the Hilbert space of a so-called “anyonic spin-chain” and nearest neighbor Hamiltonians providing a real-time evolution. There is considerable evidence
Generalized Symmetries in Condensed Matter
Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This is a brief
Fermionization of fusion category symmetries in 1+1 dimensions
We discuss the fermionization of fusion category symmetries in two-dimensional topological quantum field theories (TQFTs). When the symmetry of a bosonic TQFT is described by the representation

References

SHOWING 1-10 OF 64 REFERENCES
Topological aspects of the critical three-state Potts model
We explore the topological defects of the critical three-state Potts spin system on the torus, Klein bottle and cylinder. A complete characterization is obtained by breaking down the
Conformal Field Theory
Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a
Continuum Limits of Homogeneous Binary Trees and the Thompson Group.
TLDR
This work extends Jones's no-go example to typical elements of the so-called tensor planar algebra, and identifies an easily verified necessary condition for a continuous limit to exist.
Conformal Field Theory
© Société mathématique de France, 1989, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les
Entanglement in the XY spin chain
We consider the entanglement in the ground state of the XY model of an infinite chain. Following Bennett, Bernstein, Popescu and Schumacher, we use the entropy of a sub-system as a measure of
Scaling and Renormalization in Statistical Physics
This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. Beginning with a brief review of phase transitions in simple systems and of mean field theory,
Topological Defects on the Lattice I: The Ising model
In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer
Microscopic Models for Fusion Categories
Besides being a mathematically interesting topic on its own, subfactors have also attracted the attention of physicists, since there is a conjectured correspondence between these and Conformal Field
...
...