A Practical Introduction to Tensor Network Renormalization with TNRKit.jl

• URL: http://arxiv.org/abs/2604.06922v2
• Date: Thu, 09 Apr 2026 12:55:18 GMT
• Title: A Practical Introduction to Tensor Network Renormalization with TNRKit.jl
• Abstract summary: We present TNRKit, an open-source Julia package for Network Renormalization (TNR) of two- and three-dimensional classical statistical models.<n>It provides a framework for constructing tensor-network representations of partition functions and coarse-graining them.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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