1. ABOUT THE DATASET
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Title: Dataset for Figure 4(a,b) – Dynamics of the optimal scar state 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 4 in the paper
"ScarFinder: A detector of optimal 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 growth of bipartite entanglement entropy S_{L/2}(t) for the optimal scar initial state
of the PXP Hamiltonian with a two-site unit cell and different bond dimensions χ = 2, 4, 8, 12.
Panel (b) shows the logarithmic fidelity dynamics F_s(t) of the same optimal state at χ = 12, demonstrating
nearly perfect revivals without visible decay.

Cite as: Ren, Jie (2025): Dataset for Figure 4(a,b) – Dynamics of the optimal scar state under the PXP Hamiltonian.
University of Leeds. [Dataset3] https://doi.org/10.5518/1775

Related publication: J. Ren, A. Hallam, L. Ying, and Z. Papić, “ScarFinder: A detector of optimal scar trajectories
in quantum many-body dynamics,” PRX Quantum (2025). Accepted.

Contact: J.Ren@leeds.ac.uk


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

All files are plain-text numerical data containing columns of (time, observable value).
They can be loaded using standard scientific analysis software (Python, Julia, MATLAB, etc.).


5. METHODS
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Simulations were performed using the ScarFinder.jl framework implementing the infinite Time-Evolving Block Decimation
(iTEBD) algorithm for matrix-product states. The model studied is the PXP Hamiltonian with a two-site unit cell.
The system was initialized in the optimized scar state identified by ScarFinder, and time evolution was performed
for different bond dimensions χ = 2, 4, 8, 12. Entanglement entropy S_{L/2}(t) and fidelity F_s(t) were computed
during the evolution to characterize scar stability and quantum revivals.

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