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.

References in corpus (5)

• TensorKit.jl: A Julia package for large-scale tensor computations, with a hint of category theory
• Tensor Renormalization Group Meets Computer Assistance
• Global Tensor Network Renormalization for 2D Quantum systems: A new window to probe universal data from thermal transitions
• Deconfinement from Thermal Tensor Networks: Universal CFT signature in (2+1)-dimensional ${\mathbb{Z}}_N$ lattice gauge theory
• Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method