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21 - Tree Tensor Network States

Published online by Cambridge University Press:  18 January 2024

Tao Xiang
Affiliation:
Chinese Academy of Sciences, Beijing
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Summary

This chapter discusses the properties of tree tensor network states and the methods for evaluating the ground state and thermodynamic properties of quantum lattice models on a Bethe lattice or, more generally, a Husimi lattice. It starts with a brief discussion of the canonical form of a tree tensor network state. Then, a canonicalization scheme is proposed. To calculate the ground state through the imaginary time evolution, the full and simple update methods are introduced to renormalize the local tensors. Finally, as the correlation length of a quantum system is finite even at a critical point, an accurate and efficient method is described to compute the thermodynamic quantities of quantum lattice models on the Bethe lattice.

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Publisher: Cambridge University Press
Print publication year: 2023

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  • Tree Tensor Network States
  • Tao Xiang, Chinese Academy of Sciences, Beijing
  • Book: Density Matrix and Tensor Network Renormalization
  • Online publication: 18 January 2024
  • Chapter DOI: https://doi.org/10.1017/9781009398671.022
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  • Tree Tensor Network States
  • Tao Xiang, Chinese Academy of Sciences, Beijing
  • Book: Density Matrix and Tensor Network Renormalization
  • Online publication: 18 January 2024
  • Chapter DOI: https://doi.org/10.1017/9781009398671.022
Available formats
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Save book to Google Drive

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.

  • Tree Tensor Network States
  • Tao Xiang, Chinese Academy of Sciences, Beijing
  • Book: Density Matrix and Tensor Network Renormalization
  • Online publication: 18 January 2024
  • Chapter DOI: https://doi.org/10.1017/9781009398671.022
Available formats
×