Evenbly, G. and Vidal, G. (2015) Tensor Network Renormalization. Physical Review Letters, 115 (18). Art. No. 180405. ISSN 0031-9007. doi:10.1103/PhysRevLett.115.180405. https://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.
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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 | ||||||||||||||
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Issue or Number: | 18 | ||||||||||||||
Classification Code: | PACS numbers: 05.30.-d, 02.70.-c, 03.67.Mn, 75.10.Jm | ||||||||||||||
DOI: | 10.1103/PhysRevLett.115.180405 | ||||||||||||||
Record Number: | CaltechAUTHORS:20151119-130856215 | ||||||||||||||
Persistent URL: | https://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: | 10 Nov 2021 22:59 |
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