Multi-impurity method for the bond-weighted tensor renormalization group
smorita / bwtrg-multi-impurity
Overview
We propose a multi-impurity method for the bond-weighted tensor renormalization group (BWTRG) to compute the higher-order moment of physical quantities in a two-dimensional system. The replacement of the bond weight with an impurity matrix in a bond-weighted triad tensor network represents a physical quantity such as the magnetization and the energy. We demonstrate that the accuracy of the proposed method is much higher than the conventional tensor renormalization group for the Ising model and the five-state Potts model. Furthermore, we perform the finite-size scaling analysis and observe that the dimensionless quantity characterizing the structure of the fixed point tensor satisfies the same scaling relation in the critical region as the Binder parameter. The estimated critical temperature dependence on the bond dimension indicates that the exponent relating the correlation length to the bond dimension varies continuously with respect to the BWTRG hyperparameter. We find that BWTRG with the optimal hyperparameter is more efficient in terms of computational time than alternative approaches based on the matrix product state in estimating the critical temperature.
- URL
- https://isspns-gitlab.issp.u-tokyo.ac.jp/smorita/bwtrg-multi-impurity
- DOI
- 10.1103/PhysRevB.111.054433
- Citations
- 9 (OpenAlex, as of 2026-10-05)
- Authors
- Satoshi Morita, Naoki Kawashima
- License
- CC BY 4.0
- Keywords
- higher-order momentsIsing modelcritical temperature estimationfinite-size scalingBinder parametercorrelation lengthhyperparameter optimizationmatrix product states (keywords of the paper, from OpenAlex)
- Category
- Others
- References
- Phys. Rev. B 111, 054433 (2025)
- Contact
- smorita__at__keio.jp, kawashima__at__issp.u-tokyo.ac.jp (Please replace __at__ with @.)
Paper and citation
If you use this data, please cite the following paper.
Satoshi Morita and Naoki Kawashima, "Multi-impurity method for the bond-weighted tensor renormalization group", Physical review. B./Physical review. B 111(5) (2025). https://doi.org/10.1103/PhysRevB.111.054433
Show BibTeX
@article{Morita_2025, title={Multi-impurity method for the bond-weighted tensor renormalization group}, volume={111}, ISSN={2469-9969}, url={http://dx.doi.org/10.1103/physrevb.111.054433}, DOI={10.1103/physrevb.111.054433}, number={5}, journal={Physical Review B}, publisher={American Physical Society (APS)}, author={Morita, Satoshi and Kawashima, Naoki}, year={2025}, month=Feb }Bibliographic details and the open-access link are from OpenAlex; the BibTeX is from doi.org (as registered by the publisher).
README
Multi-impurity method for the bond-weighted tensor renormalization group
About
A multi-impurity method for the bond-weighted tensor renormalization group can accurately calculate the higher-order moments of physical quantities. This repository provides numerical results shown in our paper.
License
We would be grateful if you cite our paper when publishing results using our data.
S. Morita and N. Kawashima, "Multi-impurity method for the bond-weighted tensor renormalization group", Phys. Rev. B 111, 054433 (2025)
https://doi.org/10.1103/PhysRevB.111.054433
Folder structures
- LICENSE
- README.md
- data
- ising (Fig. 4)
- ising_T226 (Fig. 5)
- potts_Q5 (Fig. 6)
- ising_fss (Figs. 7 and 8)
- ising_tc_err (Figs. 9 and 10)
See README.md in each folder for more information on the data. Each folder also contains a sample script for plotting data and its plotting results.
Source code
The BWTRG source code for generating data in this repository will be provided upon request.
Contact
- Satoshi Morita <smorita__at__keio.jp> (Corresponding Author)
- Naoki Kawashima <kawashima__at__issp.u-tokyo.ac.jp>
please replace __at__ by @.
Links
Source: https://isspns-gitlab.issp.u-tokyo.ac.jp/smorita/bwtrg-multi-impurity README