Matrix product states and projected entangled pair states: Concepts, symmetries, theorems

  title={Matrix product states and projected entangled pair states: Concepts, symmetries, theorems},
  author={Ignacio I. Cirac and David P{\'e}rez-Garc{\'i}a and Norbert Schuch and F. Verstraete},
  journal={Reviews of Modern Physics},
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the syntax is provided by tensor networks. We review how matrix product states and projected entangled pair states describe many-body wavefunctions in terms of local tensors. These tensors express how the entanglement is routed, act as a novel type of non-local order parameter, and we describe how their… 
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