Defects in the 3-dimensional toric code model form a braided fusion 2-category
Liang Kong, Yin Tian, Zhi-Hao Zhang
Abstract
A bstract It was well known that there are e -particles and m -strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional ℤ 2 topological order. Recent mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional ℤ 2 topological order. In this work, we construct all topological defects of codimension 2 and higher, and show that they form a braided fusion 2-category satisfying a braiding non-degeneracy condition.
Topics & Concepts
PhysicsToric codeCodimensionCode (set theory)FusionTopology (electrical circuits)Topological defectTheoretical physicsPure mathematicsToric varietyConstruct (python library)Topological quantum numberTopological orderAlgebraic structures and combinatorial modelsAdvanced Combinatorial MathematicsHomotopy and Cohomology in Algebraic Topology