Improving the efficiency of variational tensor network algorithms

Glen Evenbly, Robert N C Pfeifer

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)


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 languageEnglish
Article number245118
Pages (from-to)245118-1-245118-8
Number of pages8
JournalPhysical Review B: Condensed Matter and Materials Physics
Issue number24
Publication statusPublished - 12 Jun 2014
Externally publishedYes


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