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PreprintCC BY 4.0arXiv

All-mode approach for general tensor renormalization group method

  • Katsumasa Nakayama
  • Shinji Takeda
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Abstract

We apply the stochastic all-mode technique to general coarse-graining schemes of the tensor renormalization group (TRG) approach. The technique possesses a notable characteristic of being entirely free from systematic errors which can potentially arise in the coarse-graining step, while it has statistical errors caused by random noise. The key element in our generalization is employing a method called squeezer, and the all-mode technique can be used when it is constructed. Since many TRG methods can be described in terms of the squeezers, our approach can be applicable in all such cases. In this work, we demonstrate the new method with higher-order TRG in the two- and three-dimensional Ising model.

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Cite

BibTeXRIS
BibTeX
@misc{nakayama2026allmode,
  title = {{All-mode approach for general tensor renormalization group method}},
  author = {Katsumasa Nakayama and Shinji Takeda},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02394},
  eprint = {2610.02394},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02394},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - All-mode approach for general tensor renormalization group method
AU  - Katsumasa Nakayama
AU  - Shinji Takeda
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2610.02394
UR  - https://arxiv.org/abs/2610.02394
AB  - We apply the stochastic all-mode technique to general coarse-graining schemes of the tensor renormalization group (TRG) approach. The technique possesses a notable characteristic of being entirely free from systematic errors which can potentially arise in the coarse-graining step, while it has statistical errors caused by random noise. The key element in our generalization is employing a method called squeezer, and the all-mode technique can be used when it is constructed. Since many TRG methods can be described in terms of the squeezers, our approach can be applicable in all such cases. In this work, we demonstrate the new method with higher-order TRG in the two- and three-dimensional Ising model.
ER  -