1. ABOUT THE DATASET
--------------------

Title: Dataset for Figure 5(a,b) – Late-time dynamics of optimized scar states under the PXP Hamiltonian

Creator(s): Jie Ren
Organisation(s): University of Leeds
Rights-holder(s): Unless otherwise stated, Copyright 2025 University of Leeds
Publication Year: 2025

Description:
This dataset contains numerical data corresponding to panels (a) and (b) of Figure 5 in the paper
"ScarFinder – Detection of quantum many-body scar trajectories in Quantum Many-Body Dynamics"
by J. Ren, A. Hallam, L. Ying, and Z. Papić (PRX Quantum, 2025, Accepted).

Panel (a) presents the late-time entanglement entropy growth S_{L/2}(t) for the optimized scar initial
states of the PXP Hamiltonian with a three-site unit cell, simulated using iTEBD for different bond
dimensions χ = 2, 4, 8, 12. Increasing χ systematically suppresses entanglement growth and stabilizes
periodic dynamics.
Panel (b) shows the logarithmic fidelity dynamics F_s(t) for the optimized state at χ = 12, computed
from the dominant eigenvalue of the MPS transfer matrix, exhibiting stable and periodic revivals.

Cite as: Ren, Jie (2025): Dataset for Figure 5(a,b) – Late-time dynamics of optimized scar states under the PXP Hamiltonian.
University of Leeds. [Dataset] https://doi.org/10.5518/1775

Related publication: J. Ren, A. Hallam, L. Ying, and Z. Papić, “ScarFinder – Detection of quantum many-body scar trajectories in Quantum Many-Body Dynamics,” PRX Quantum (2025). Accepted.

Contact: J.Ren@leeds.ac.uk


2. TERMS OF USE
---------------
Copyright 2025 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
----------------------------------
Title: ScarFinder – Detection of quantum many-body scar trajectories in Quantum Many-Body Dynamics
Dates: 2023–2025
Funding organisation: Leverhulme Trust; EPSRC
Grant no.: RL-2019-015; EP/Z533634/1


4. CONTENTS
-----------
File listing:
EE-2.dat – Entanglement entropy S_{L/2}(t) for χ = 2 (Fig. 5a)
EE-4.dat – Entanglement entropy S_{L/2}(t) for χ = 4 (Fig. 5a)
EE-8.dat – Entanglement entropy S_{L/2}(t) for χ = 8 (Fig. 5a)
EE-12.dat – Entanglement entropy S_{L/2}(t) for χ = 12 (Fig. 5a)
Fid-2.dat – Fidelity F_s(t) for χ = 2 (not plotted, provided for completeness)
Fid-4.dat – Fidelity F_s(t) for χ = 4 (not plotted, provided for completeness)
Fid-8.dat – Fidelity F_s(t) for χ = 8 (not plotted, provided for completeness)
Fid-12.dat – Fidelity F_s(t) for χ = 12 (Fig. 5b)

All files are plain-text numerical data containing two columns: (time, observable value).
Files can be loaded directly in common analysis environments (Python, Julia, MATLAB, etc.).


5. METHODS
----------
Simulations were performed using the ScarFinder.jl framework implementing the infinite Time-Evolving Block Decimation
(iTEBD) algorithm for matrix-product states. The system studied is the PXP Hamiltonian with a three-site unit cell.
The initial states were the optimized scar states identified by ScarFinder. Time evolution was performed for bond
dimensions χ = 2, 4, 8, 12, and observables S_{L/2}(t) and F_s(t) were computed to assess entanglement growth and
revival behavior.

All simulations were carried out on the Aire HPC cluster at the University of Leeds using Julia 1.10 and ITensorMPS.jl.
