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The mechanism for anionic chain-growth polymerization involves initiation, propagation, and termination steps. In the initiation step, a nucleophilic anion, such as butyl lithium, initiates the polymerization process by attacking the π bond of the vinylic monomer. As a result, a carbanion, stabilized by the electron‐withdrawing group, is generated. The resulting carbanion acts as a Michael donor in the propagation step and attacks the second vinylic monomer, which acts as a Michael...
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The skeletal structure of polymers synthesized via radical polymerization is always branched. For example, the polymerization of ethylene by radical polymerization results in a low-density grade of polyethylene with a heavily branched skeletal structure. Here, the radical site abstracts hydrogen from the growing chain, and the radical site shifts from the end (a primary carbon center) to anywhere within the growing chain (a secondary carbon center). Consequently, the part of the chain from the...
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The radical chain-growth polymerization mechanism consists of three steps: initiation, propagation, and termination of polymerization. The polymerization initiates when a free radical generated from the radical initiator adds to the unsaturated bond in the monomer. The unpaired electron of the free radical and one π electron in the unsaturated bond creates a σ bond between the free radical and the monomer. As a result, the other π electron in the unsaturated bond converts this species into...
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The cationic polymerization mechanism consists of three steps: initiation, propagation, and termination. In the initiation step of the polymerization process, the π bond of a monomer gets protonated by the Lewis acid catalyst, which is formed from boron trifluoride and water. The protonation of the π bond generates a carbocation stabilized by the electron‐donating group. In the propagation step, the π bond of the second monomer acts as a nucleophile and attacks the...
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The polymerization process that involves carbanion as an intermediate is called anionic polymerization. It is also a type of addition or chain-growth polymerization. Anionic polymerization gets initiated by a strong nucleophile such as an organolithium or a Grignard reagent. The most commonly used initiator for anionic polymerization is butyl lithium. Monomers involved in anionic polymerization must possess a vinyl group bonded to one or two electron-withdrawing groups. For instance,...
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Chain-growth or addition polymerization is successive addition reactions of monomers with a polymer chain. In radical chain-growth polymerization, the reaction proceeds via a free-radical intermediate. The free radical is formed from radical initiators, which spontaneously generate free radicals by homolytic fission. Organic peroxides (such as dibenzoyl peroxide, as shown in Figure 1) or azo compounds are popular radical initiators. A low concentration ratio of radical initiator to monomer is...
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ℤ3 parafermionic chain emerging from Yang-Baxter equation.

Li-Wei Yu1, Mo-Lin Ge1

  • 1Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin 300071, China.

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|February 24, 2016
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Summary
This summary is machine-generated.

We introduce a 1D Z3 parafermionic model, a generalization of the Z2 Kitaev model, derived from the Yang-Baxter equation. This model exhibits triple degenerate ground states and topological properties, extending Majorana models to SU(3) systems.

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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.