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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Mathematical Physics

Background:

  • Fusion categories generalize finite group symmetries to include non-invertible operations.
  • The Haagerup fusion category is a novel mathematical structure not derived from finite groups or affine Lie algebras.

Purpose of the Study:

  • To numerically investigate an anyon chain model based on the Haagerup fusion category.
  • To identify the long-distance behavior and emergent symmetries of such a system.
  • To explore the first instance of conformal field theories with exotic generalized symmetries.

Main Methods:

  • Numerical simulations of an anyon chain.
  • Analysis of the system's properties in the long-distance limit.
  • Identification of the emergent conformal field theory and its central charge.

Main Results:

  • Evidence suggests the anyon chain leads to a conformal field theory in the long-distance limit.
  • The emergent conformal field theory possesses a central charge of approximately 2.
  • This work presents the first example of conformal field theories with truly exotic generalized symmetries.

Conclusions:

  • The Haagerup fusion category provides a basis for exotic generalized symmetries in physical systems.
  • The numerical study confirms the emergence of a specific conformal field theory from this category.
  • This research opens new avenues for exploring novel quantum phases and their symmetries.