Ribbon operators in the Semidual lattice code model

2024/01/24 by Soglohu, Fred, Osei, Prince K., Osumanu, Abdulmajid · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Strongly Correlated Electrons (cond-mat.str-el)

paper · doi:10.48550/arxiv.2401.13774

Abstract

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^cop\lrbicross H or M(H)^op depending on their chirality or local orientation.

Cited by

• Higher lattice gauge theory from representations of 2-groups and 3+1D topological phases

Related

• Semidual Kitaev lattice model and tensor network representation
• Band representations in Strongly Correlated Settings: The Kitaev Honeycomb Model
• A non-semisimple Kitaev lattice model
• Ribbon Schur Operators
• The ribbon category framework for topological quantum computing