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.

Strongly Correlated Electrons (cond-mat.str-el); Statistical Mechanics (cond-mat.stat-mech); Mathematical Software (cs.MS); Quantum Physics (quant-ph)

arXiv:2604.06922 [cond-mat.str-el]

(or arXiv:2604.06922v4 [cond-mat.str-el] for this version)