1. ABOUT THE DATASET
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Title: Supporting data for "Spectral signatures of nonstabilizerness and criticality in infinite matrix product states"

Creator(s): Andrew Hallam, Ryan Smith, Zlatko Papic

Organisation(s): School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom.

Rights-holder(s):Unless otherwise stated, Copyright 2026 University of Leeds

Publication Year: 2026

Description: Data for VUMPS, MPS and exact diagonalization results.  The dataset includes seperate data files for each figure in the manuscript, in the .txt, .mat and .pkl file types which can be loaded into python.

Cite as: Hallam, Andrew, Smith, Ryan and Papic, Zlatko (2026) Supporting data for "Spectral signatures of nonstabilizerness and criticality in infinite matrix product states". University of Leeds. [Dataset] https://doi.org/10.5518/1852

Related publication: Andrew Hallam, Ryan Smith, Zlatko Papic, Spectral signatures of nonstabilizerness and criticality in infinite matrix product states, Physical Review B (2026) (Accepted). https://doi.org/10.1103/77wh-qv29

Contact: 
Corresponding author: Ryan Smith
Email. ll17rps@leeds.ac.uk
Affliation: School of Physics and Astronomy, University of Leeds, UK


2. TERMS OF USE
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Copyright 2026 University of Leeds. 
Unless otherwise stated, this dataset is licensed under a Creative Commons Attribution 4.0 International Licence: https://creativecommons.org/licenses/by/4.0/


3. PROJECT AND FUNDING INFORMATION
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Title: Spectral signatures of nonstabilizerness and criticality in infinite matrix product states


Funding organisation: Leverhulme Trust

Grant no.: RL-2019-015

Funding organisation: EPSRC

Grant no.: EP/Z533634/1, UKRI1337

Funding organisation: Kavli Institute for Theoretical Physics

Grant no.: NSF PHY-2309135

Acknowledgements:
The Erwin Schrödinger International Institute for Mathematics and Physics.


4. CONTENTS
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Data is included either as plain text columns stored in the .txt file type or a dictionary stored in the .pkl or.mat file type.
The files can be read using any standard data analysis software (Python, Julia, MATLAB, etc.).

Each numbered folder corresponds to a figure in the publication:

| Folder | Content summary 
|--------|---------------------------------------------------------------------------------------------------------------------------------------------------
| fig_2/ | Contains 4 .txt files with the raw data to plot Figures 2(a), 2(b), 2(c) and the inset in 2(b).
|        | The .txt files are named as Fig_{figure number}{panel label}.txt
|--------|---------------------------------------------------------------------------------------------------------------------------------------------------
| fig_3/ | Contains 3 .txt files with the raw data to plot Figures 3(a), 3(b) and 3(c).
|        | The .txt files are named as Fig_{figure number}{panel label}.txt
|--------|---------------------------------------------------------------------------------------------------------------------------------------------------
| fig_4/ | Contains 1 .mat file with the raw data to plot Figures 4(a), 4(b) and 4(c).
|--------|---------------------------------------------------------------------------------------------------------------------------------------------------
| fig_5/ | Contains 1 .mat file with the raw data to plot Figures 5(a), 5(b) and 5(c).
|--------|---------------------------------------------------------------------------------------------------------------------------------------------------
| fig_6/ | Contains 1 .txt file with the raw data to plot Figure 6.
|--------|---------------------------------------------------------------------------------------------------------------------------------------------------
| fig_7/ | Contains 6 .txt files with the raw data to plot Figures 7(a), 7(b), 7(c) and 7(d).
|        | The .txt files labelled as Fig_{figure number}{panel label}.txt correspond to each figure.
|        | The .txt files labelled as Fig_{figure number}d_crit{index}.txt correspond to the following critical points in Figure 7(d):
|        |   - index=1 corresponds to mu=-1
|        |   - index=2 corresponds to mu=-1/2
|        |   - index=3 corresponds to mu=1
|--------|---------------------------------------------------------------------------------------------------------------------------------------------------
| fig_8/ | Contains 2 .pkl files and 1 .txt file with the raw data to plot Figures 8(a), 8(b) and 8(c).
|        | The .pkl files labelled as Fig_{figure number}{panel label}.pkl correspond to the appropriate figure.
|        | The .txt file labelled as Fig_{figure number}{panel label}.txt correspond to Figure 8(c).
|--------|---------------------------------------------------------------------------------------------------------------------------------------------------
| fig_9/ | Contains 1 .mat file with the raw data to plot Figures 9(a), 9(b) and 9(c).
|--------|---------------------------------------------------------------------------------------------------------------------------------------------------

5. METHODS
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The data was generated using VUMPS, other infinite matrix product state techniques and by exact diagonalization.