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Improving the efficiency of variational tensor network algorithms

Evenbly, Glen and Pfeifer, Robert N. C. (2014) Improving the efficiency of variational tensor network algorithms. Physical Review B, 89 (24). Art. No. 245118. ISSN 1098-0121. http://resolver.caltech.edu/CaltechAUTHORS:20140807-101932641

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1310.8023arXivDiscussion Paper
http://dx.doi.org/10.1103/PhysRevB.89.245118 DOIArticle
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.89.245118PublisherArticle
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.89.245118#supplementalPublisherSupplemental Material
Additional Information:© 2014 American Physical Society. Received 7 February 2014; revised manuscript received 13 May 2014; published 12 June 2014. G.E. is supported by the Sherman Fairchild foundation. R.N.C.P. gratefully acknowledges the Ontario Ministry of Research and Innovation Early Researcher Awards for financial support. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Ontario Ministry of Research and Innovation Early Researcher AwardsUNSPECIFIED
Government of CanadaUNSPECIFIED
Industry CanadaUNSPECIFIED
Province of Ontario Ministry of Research and InnovationUNSPECIFIED
Classification Code:PACS: 05.30.−d, 02.70.−c, 75.10.Jm, 04.60.Pp
Record Number:CaltechAUTHORS:20140807-101932641
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20140807-101932641
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:48177
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Aug 2014 20:59
Last Modified:07 Aug 2014 20:59

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