Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices

Hui Hai Zhao, Zhi Yuan Xie, Tao Xiang, Masatoshi Imada

Research output: Contribution to journalArticlepeer-review

30 Citations (Scopus)


We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.

Original languageEnglish
Article number125115
JournalPhysical Review B
Issue number12
Publication statusPublished - 2016 Mar 9
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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