A Practical Introduction to Tensor Network Renormalization with TNRKit.jl
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.
Keywords
Cite
@article{arxiv.2604.06922,
title = {A Practical Introduction to Tensor Network Renormalization with TNRKit.jl},
author = {Victor Vanthilt and Adwait Naravane and Chenqi Meng and Atsushi Ueda},
journal= {arXiv preprint arXiv:2604.06922},
year = {2026}
}