### Abstract

We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed tensor network T, we prove that if the environment of a single tensor from the network can be evaluated with computational cost κ, then the environment of any other tensor from T can be evaluated with identical cost κ. Moreover, we describe how the set of all single tensor environments from T can be simultaneously evaluated with fixed cost 3κ. The usefulness of these results, which are applicable to a variety of tensor network methods, is demonstrated for the optimization of a multiscale entanglement renormalization Ansatz for the ground state of a one-dimensional quantum system, where they are shown to substantially reduce the computation time.

Original language | English |
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Article number | 245118 |

Pages (from-to) | 245118-1-245118-8 |

Number of pages | 8 |

Journal | Physical Review B: Condensed Matter and Materials Physics |

Volume | 89 |

Issue number | 24 |

DOIs | |

Publication status | Published - 12 Jun 2014 |

Externally published | Yes |

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## Cite this

*Physical Review B: Condensed Matter and Materials Physics*,

*89*(24), 245118-1-245118-8. [245118]. https://doi.org/10.1103/PhysRevB.89.245118