Defects in the 3-dimensional toric code model form a braided fusion 2-category

Liang Kong; Yin Tian; Zhi-Hao Zhang

doi:10.1007/jhep12(2020)078

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arXiv · 2009.06564

Defects in the 3-dimensional toric code model form a braided fusion 2-category

Liang Kong·Yin Tian·Zhi-Hao Zhang

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Abstract

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 $\mathbb{Z}_2$ topological order. Recent mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional $\mathbb{Z}_2$ 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.

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Liang Kong, Yin Tian, Zhi-Hao Zhang. 2020-09-14. Defects in the 3-dimensional toric code model form a braided fusion 2-category. https://doi.org/10.1007/jhep12(2020)078

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