A Practical Introduction to Tensor Network Renormalization with TNRKit.jl
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910148348346368 |
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| author | Vanthilt, Victor Naravane, Adwait Meng, Chenqi Ueda, Atsushi |
| author_facet | Vanthilt, Victor Naravane, Adwait Meng, Chenqi Ueda, Atsushi |
| contents | We present TNRKit, an open-source Julia package for Tensor Network Renormalization (TNR) of two- and three-dimensional classical statistical models and Euclidean lattice field theories. Built on top of TensorKit, it provides a symmetry-aware framework for constructing tensor-network representations of partition functions and coarse-graining them using methods such as TRG, HOTRG, and LoopTNR. Beyond thermodynamic quantities, the package enables the extraction of universal conformal data -- including scaling dimensions and the central charge -- directly from fixed-point tensors. TNRKit is designed with both usability and extensibility in mind, offering a practical platform for applying, benchmarking, and developing modern tensor renormalization algorithms. This paper also serves as a self-contained introduction to the TNR framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06922 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Practical Introduction to Tensor Network Renormalization with TNRKit.jl Vanthilt, Victor Naravane, Adwait Meng, Chenqi Ueda, Atsushi Strongly Correlated Electrons Statistical Mechanics Mathematical Software Quantum Physics We present TNRKit, an open-source Julia package for Tensor Network Renormalization (TNR) of two- and three-dimensional classical statistical models and Euclidean lattice field theories. Built on top of TensorKit, it provides a symmetry-aware framework for constructing tensor-network representations of partition functions and coarse-graining them using methods such as TRG, HOTRG, and LoopTNR. Beyond thermodynamic quantities, the package enables the extraction of universal conformal data -- including scaling dimensions and the central charge -- directly from fixed-point tensors. TNRKit is designed with both usability and extensibility in mind, offering a practical platform for applying, benchmarking, and developing modern tensor renormalization algorithms. This paper also serves as a self-contained introduction to the TNR framework. |
| title | A Practical Introduction to Tensor Network Renormalization with TNRKit.jl |
| topic | Strongly Correlated Electrons Statistical Mechanics Mathematical Software Quantum Physics |
| url | https://arxiv.org/abs/2604.06922 |