Tensor-product representations for string-net condensed states

Citation Gu, Zheng-Cheng et al. " Tensor-product representations for string-net condensed states. Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We show that general string-net condensed states have a natural representation in terms of tensor product states ͑TPSs͒. These TPSs are built from local tensors. They can describe both states with short-range entangle-ment ͑such as the symmetry-breaking states͒ and states with long-range entanglement ͑such as string-net condensed states with topological/quantum order͒. 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 TPSs are fixed points under a certain wave-function renormalization-group transformation for quantum states.