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23 - Coarse-Graining Tensor Renormalization

Published online by Cambridge University Press:  18 January 2024

Tao Xiang
Affiliation:
Chinese Academy of Sciences, Beijing
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Summary

Coarse-graining renormalization aims to reformulate a tensor network model with a coarse-grained one at a larger scale. It has attracted particular attention in recent years because it opens a new avenue to unveil the entanglement structure of a tensor network model under the scaling transformation. This chapter reviews and compares the tensor renormalization group (TRG) and other coarse-graining methods developed in the past two decades. The methods can be divided into two groups according to whether or not the renormalization effect of the environment tensors is incorporated in the optimization of local tensors. The local optimization methods include TRG, HOTRG (a variant of TRG based on the higher-order singular value decomposition), tensor network renormalization (TNR), and loop-TNR. The global optimization methods include the second renormalized TRG and HOTRG, referred to as SRG and HOSRG, respectively. Among all these coarse-graining methods, HOTRG and HOSRG are the only two that can be readily extended and efficiently applied to three-dimensional classical or two-dimensional quantum lattice models.

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Publisher: Cambridge University Press
Print publication year: 2023

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  • Coarse-Graining Tensor Renormalization
  • Tao Xiang, Chinese Academy of Sciences, Beijing
  • Book: Density Matrix and Tensor Network Renormalization
  • Online publication: 18 January 2024
  • Chapter DOI: https://doi.org/10.1017/9781009398671.024
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  • Coarse-Graining Tensor Renormalization
  • Tao Xiang, Chinese Academy of Sciences, Beijing
  • Book: Density Matrix and Tensor Network Renormalization
  • Online publication: 18 January 2024
  • Chapter DOI: https://doi.org/10.1017/9781009398671.024
Available formats
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To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Coarse-Graining Tensor Renormalization
  • Tao Xiang, Chinese Academy of Sciences, Beijing
  • Book: Density Matrix and Tensor Network Renormalization
  • Online publication: 18 January 2024
  • Chapter DOI: https://doi.org/10.1017/9781009398671.024
Available formats
×