A Practical Introduction to Tensor Network Renormalization with TNRKit.jl

TL;DR

TNRKit.jl is an open-source Julia package that facilitates tensor network renormalization of classical models and lattice theories, enabling extraction of universal conformal data.

Contribution

It introduces TNRKit, a flexible, symmetry-aware platform for tensor network coarse-graining and data extraction, with a comprehensive introduction to TNR methods.

Findings

Supports 2D and 3D models and theories.

Enables extraction of conformal data from fixed-point tensors.

Provides a practical, extensible framework for tensor renormalization.

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.