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Critical Lattice Model for a Haagerup Conformal Field Theory.

Robijn Vanhove1, Laurens Lootens1, Maarten Van Damme1

  • 1Department of Physics and Astronomy, Ghent University, Krijgslaan 281, S9, B-9000 Ghent, Belgium.

Physical Review Letters
|June 24, 2022
PubMed
Summary

Researchers constructed a critical classical lattice model using the Haagerup fusion category, providing numerical evidence for a Haagerup conformal field theory (CFT) with central charge two. This work offers a counterexample to a common conjecture in CFT.

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Area of Science:

  • Theoretical physics
  • Condensed matter physics
  • Quantum field theory

Background:

  • Conformal field theories (CFTs) are crucial in understanding critical phenomena.
  • The Haagerup fusion category (H3) is a key structure in category theory with potential applications in physics.
  • Standard methods for constructing rational CFTs exist but may not cover all cases.

Purpose of the Study:

  • To construct a critical classical lattice model using the Haagerup fusion category (H3).
  • To provide numerical evidence for a Haagerup conformal field theory (CFT) with central charge c=2.
  • To investigate the relationship between lattice models, CFTs, and modular tensor categories.

Main Methods:

  • Utilizing the formalism of strange correlators for model construction.
  • Employing finite entanglement scaling for numerical evidence.
  • Performing exact diagonalization of the transfer matrix to obtain CFT spectra.
  • Identifying conformal towers with topological sectors.

Main Results:

  • Successful construction of a 2D critical classical lattice model with H3 input data.
  • Compelling numerical evidence supporting a Haagerup CFT with central charge c=2.
  • Numerical determination of generalized twisted CFT spectra and separation of conformal towers.
  • Demonstration that the model can be derived from a larger lattice model via an orbifold procedure.

Conclusions:

  • The study provides a concrete example of a CFT constructed from non-standard input data.
  • The findings challenge the conjecture that all rational CFTs can be built using established algebraic methods.
  • This work opens new avenues for exploring CFTs beyond traditional constructions.