We show that general string-net condensed states have a natural representation in terms of tensor product states (TPS) . These TPS's are built from local tensors. They can describe both states with short-range entanglement (such as the symmetry breaking states) and states with long-range entanglement (such as string-net condensed states with topological/quantum order). The tensor product representation provides a kind of 'mean-field' description for topologically ordered states and could be a powerful way to study quantum phase transitions between such states. As an attempt in this direction, we show that the constructed TPS's are fixed-points under a certain wave-function renormalization group transformation for quantum states.
@article{arxiv.0809.2821,
title = {Tensor-product representations for string-net condensed states},
author = {Zheng-Cheng Gu and Michael Levin and Brian Swingle and Xiao-Gang Wen},
journal= {arXiv preprint arXiv:0809.2821},
year = {2009}
}