Data for "Entanglement across scales: Quantics tensor trains as a natural framework for renormalization"

This dataset contains the Supplemental Material, original figures, numerical (raw) data and plot scripts to reproduce the results from the publication "Entanglement across scales: Quantics tensor trains as a natural framework for renormalization" at Physical Review Research. The preprint is available on arXiv. All materials required to regenerate the figures and verify the numerical results are included. Information is also provided in the README.txt.

Background

This study looks at how entanglement behaves across different length scales—a part of quantum physics that hasn’t been explored as much as entanglement between individual sites or particles. The authors show that the quantics tensor train (QTT) decomposition, which is related to matrix product states, naturally fits the role of a renormalization group method. By connecting a cyclic-reduction real-space renormalization procedure to the QTT framework, they establish a clear link between the QTT bond dimension (which measures entanglement across scales) and the number of effective couplings that appear at each coarse-graining step. The dataset contains numerical and semi-analytical results for a one-dimensional tight-binding model with n-th-nearest-neighbor hopping, where the structure of the renormalization flow mirrors the QTT bond dimension of the Green’s function.

Structure

The dataset is organized into:

• figure_X/ directories:
  Each contains

  • the original figure (figure_X.pdf),

  • the plot script used to generate it (.jl),

  • and the corresponding raw numerical data. In some cases, additional subdirectories store data for different parameter settings.
    
    

• Supplemental_Material/: Contains two Mathematica notebooks with the detailed analytical derivations referenced in the paper.

Technical Details

The numerical computations and plotting scripts were created using:

• Julia (v1.10.10) with the following non-standard packages:
  DelimitedFiles v1.9.1, CairoMakie v0.15.5, HDF5 v0.17.2, LaTeXStrings v1.4.0, CurveFit v0.6.1, QuadGK v2.11.2, DataFrames v1.8.1
  The data generation used the publicly available tensor libraries tensor4all and ITensors.
• Wolfram Mathematica (v14.1) for the analytical calculations contained in the supplemental notebooks.

Licensing

The CC-BY 4.0 license applies to all the data and PDF files. All distributed code is licensed under the MIT license.