# Tensor Network

The tensor network formalism provides an efficient representation of many-body entangled wave functions satisfying an area law and therefore has become a powerful tool in both the analytical and numerical study of strongly interacting condensed matter systems. We are interested in using the tensor network representation to study systems with nontrivial topological order. In particular, we focus on questions like: what kind of topological order can be represented with tensors, how to extract the topological order encoded in local tensors and in general how to simulate strongly interacting systems in a more efficient way.

- "Classification of Gapped Symmetric Phases in One-dimensional Spin Systems", Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen,
*Phys. Rev. B*83, 035107 (2011)(Classification of 1D SPT phases using the matrix product state formalism.) - "Tensor Product Representation of Topological Ordered Phase: Necessary Symmetry Conditions", Xie Chen, Bei Zeng, Zheng-Cheng Gu, Isaac L. Chuang, Xiao-Gang Wen,
*Phys. Rev. B*82, 165119 (2010)(Study the stability in the tensor network representation of Z2 topological order and find a necessary symmetry condition.) - "Boson condensation and instability in the tensor network representation of string-net states", Sujeet Shukla, Mehmet Burak Sahinoglu, Frank Pollmann, Xie Chen,
*Phys. Rev. B*98, 125112 (2018).

(Study the stability in the tensor network representation of general string net states and find the necessary symmetry condition) - "Towards gauging time reversal symmetry in tensor network states", Xie Chen, Ashvin Vishwanath,
*Phys. Rev. X***5**, 041034 (2015)(Introduce the notion of â€˜gauging' time reversal symmetry in the tensor network formalism and demonstrate how it can be used to detect topological order.) - "Matrix Product Representation of Locality Preserving Unitaries", Mehmet Burak Sahinoglu, Sujeet Shukla, Feng Bi, Xie Chen,
*Phys. Rev. B*98, 245122 (2018).

(Translation invariant matrix product unitary operators are locality preserving.)