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 ℤ2 topological order. Recent mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional ℤ2 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.
The
$${{\bf{Z}}}_{{\bf{2}}}$$
Z
2
toric-code and the double-semion topological order of hardcore Bose-Hubbard-type models in the strong-interaction limit
