# Generalizations and limitations of string-net models

@article{Lin2014GeneralizationsAL, title={Generalizations and limitations of string-net models}, author={C. Lin and Michael A. Levin}, journal={Physical Review B}, year={2014}, volume={89}, pages={195130} }

We ask which topological phases can and cannot be realized by exactly soluble string-net models. We answer this question for the simplest class of topological phases, namely those with abelian braiding statistics. Specifically, we find that an abelian topological phase can be realized by a string-net model if and only if (i) it has a vanishing thermal Hall conductance and (ii) it has at least one Lagrangian subgroup --- a subset of quasiparticles with particular topological properties… Expand