Ribbon operators in the Semidual lattice code model

In this work, we provide a rigorous definition of ribbon operators in the Semidual Kitaev lattice model and study their properties. These operators are essential for understanding quasi-particle excitations within topologically ordered systems. We show that the ribbon operators generate quasi-partic...

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Bibliographic Details
Main Authors Soglohu, Fred, Osei, Prince K, Osumanu, Abdulmajid
Format Journal Article
LanguageEnglish
Published 24.01.2024
Subjects
Mathematics - Mathematical Physics
Physics - High Energy Physics - Theory
Physics - Mathematical Physics
Physics - Strongly Correlated Electrons
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Summary:In this work, we provide a rigorous definition of ribbon operators in the Semidual Kitaev lattice model and study their properties. These operators are essential for understanding quasi-particle excitations within topologically ordered systems. We show that the ribbon operators generate quasi-particle excitations at the ends of the ribbon and reveal themselves as irreducible representations of the Bicrossproduct quantum group $M(H)=H^{\text{cop}}\lrbicross H$ or $M(H)^{\text{op}}$ depending on their chirality or local orientation.
DOI:10.48550/arxiv.2401.13774