A Practical Introduction to Tensor Network Renormalization with TNRKit.jl
This provides a practical tool for researchers in computational physics to apply and develop tensor renormalization algorithms, though it is incremental as it builds on existing methods.
The authors introduced TNRKit.jl, an open-source Julia package for Tensor Network Renormalization (TNR) to analyze classical statistical models and lattice field theories, enabling the extraction of universal conformal data like scaling dimensions and central charge from fixed-point tensors.
We present TNRKit.jl, 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.jl\cite{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.jl 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.