Tensor-product representations for string-net condensed states

Zheng Cheng Gu, Michael Levin, Brian Swingle, Xiao Gang Wen

Research output: Contribution to journalArticlepeer-review

97 Scopus citations


We show that general string-net condensed states have a natural representation in terms of tensor product states (TPSs). These TPSs 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 TPSs are fixed points under a certain wave-function renormalization-group transformation for quantum states.

Original languageEnglish
Article number085118
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number8
StatePublished - 18 Mar 2009
Externally publishedYes


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