Numerical Evidence for a Haagerup Conformal Field Theory

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.