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Tensor Network Renormalization

Evenbly, G. and Vidal, G. (2015) Tensor Network Renormalization. Physical Review Letters, 115 (18). Art. No. 180405. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20151119-130856215

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Abstract

We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of tensors), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevLett.115.180405DOIArticle
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.180405PublisherArtile
http://journals.aps.org/prl/supplemental/10.1103/PhysRevLett.115.180405/SuppMaterial.pdfPublisherSupplemental Material
Additional Information:© 2015 American Physical Society. (Received 21 April 2015; published 29 October 2015) We thank Z.-C. Gu and X.-G. Wen for clarifying aspects of their TEFR approach [7]. G. E. is supported by the Sherman Fairchild Foundation. G. V. acknowledges support by the John Templeton Foundation and the NSERC. The authors also acknowledge support by the Simons Foundation (the Many Electron Collaboration). 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:Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
John Templeton FoundationUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Simons FoundationUNSPECIFIED
Industry CanadaUNSPECIFIED
Ministry of Research and Innovation, Province of Ontario, CanadaUNSPECIFIED
Classification Code:PACS numbers: 05.30.-d, 02.70.-c, 03.67.Mn, 75.10.Jm
Record Number:CaltechAUTHORS:20151119-130856215
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20151119-130856215
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:62243
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:19 Nov 2015 21:22
Last Modified:19 Nov 2015 21:22

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