2013/10/31 by Glen Evenbly, Robert N. C. Pfeifer
Physics and Astronomy · #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.89.245118
published as Phys. Rev. B 89, 245118 (2014) · 12 pages, 8 figures, RevTex 4.1, includes reference implementation. Software updated to v1.02: Resolved two scenarios in which multienv would generate errors for valid inputs
arxiv created 2015/12/23 · arxiv updated 2015/12/25
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 Multi-scale Entanglement Renormalization Ansatz (MERA) for the ground state of a 1D quantum system, where they are shown to substantially reduce the computation time.