The structure of string-net lattice models, relevant as examples of topological phases, leads to a remarkably simple way of expressing their ground states as a tensor network constructed from the basic data of the underlying tensor categories. The construction highlights the importance of the fat lattice to understand these models.
@article{arxiv.0809.2393,
title = {Explicit tensor network representation for the ground states of string-net models},
author = {O. Buerschaper and M. Aguado and G. Vidal},
journal= {arXiv preprint arXiv:0809.2393},
year = {2009}
}