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Published October 30, 2015 | Published + Supplemental Material
Journal Article Open

Tensor Network Renormalization

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.

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.

Attached Files

Published - PhysRevLett.115.180405.pdf

Supplemental Material - SuppMaterial.pdf

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Additional details

Created:
August 20, 2023
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October 25, 2023