ℤ3 parafermionic chain emerging from Yang-Baxter equation.

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory
• Mathematical Physics

Background:

• The Yang-Baxter equation is crucial for constructing solvable models in quantum mechanics.
• Kitaev and Majorana models are foundational for understanding topological phases and quantum computing.
• Generalizing Z2 models to higher symmetries like Z3 is an active area of research.

Purpose of the Study:

• To construct and analyze a 1D Z3 parafermionic model.
• To explore its relationship with the Yang-Baxter equation and existing Z2 models.
• To investigate its unique properties, including degeneracy and topological characteristics.

Main Methods:

• Construction of the 1D Z3 parafermionic model using solutions to the Yang-Baxter equation.
• Expression of the model using three types of fermions.
• Definition of a novel 3-body Hamiltonian (H123) to illustrate parafermionic algebra.
• Analysis of ground state degeneracy and topological winding numbers.
• Identification of symmetry operators protecting the system's properties.

Main Results:

• The 1D Z3 parafermionic model possesses triple degenerate ground states and a non-trivial topological winding number.
• This model is a direct generalization of the 1D Z2 Kitaev model, both derivable from the Yang-Baxter equation.
• A new 3-body Hamiltonian (H123) demonstrates parafermionic tripling, distinct from Majorana doubling.
• The triple degeneracy in H123 is protected by generalized symmetry operators (ω-parity and emergent parafermionic operator).
• Both the Z3 model and H123 can be interpreted as SU(3) models, generalizing SU(2) Majorana models.

Conclusions:

• The 1D Z3 parafermionic model, derived from the Yang-Baxter equation, successfully generalizes the 1D Z2 Kitaev model.
• The novel H123 Hamiltonian provides an intuitive understanding of parafermionic tripling and its associated symmetries.
• These SU(3) models represent a significant advancement in generalizing Majorana models, with implications for topological phases and quantum information theory.