1. ABOUT THE DATASET
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Title: Dataset for Figure 6(a,b) – Poincaré sections of TDVP and ScarFinder trajectories

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 6 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).

The data represent Poincaré sections comparing trajectories obtained via the Time-Dependent Variational
Principle (TDVP) and the ScarFinder algorithm for the PXP Hamiltonian. Both trajectories originate from
the same initial condition in the parameter space (θ₁, θ₃), but evolve differently:
  - Panel (a) and (b): Blue points show the TDVP trajectory, which traces a regular orbit within the stable island.
  - Orange points show the ScarFinder trajectory, which rapidly converges toward the center of the stable island,
    corresponding to the robust scar trajectory previously identified as the “*-state.”

Cite as: Ren, Jie (2025): Dataset for Figure 6(a,b) – Poincaré sections of TDVP and ScarFinder trajectories.
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
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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:
PXP-01.dat – Coordinates of the TDVP trajectory (blue points) in Fig. 6(a,b), representing (θ₁/π, θ₃/π) for each iteration.
PXP-02.dat – Coordinates of the ScarFinder trajectory (orange points) in Fig. 6(a,b), representing (θ₁/π, θ₃/π) with iteration indices.

Each file contains two columns corresponding to the angular coordinates of the trajectory in the reduced phase-space section.
Data can be visualized using standard plotting tools (Python, Julia, MATLAB, etc.).


5. METHODS
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The data were generated using the ScarFinder.jl package and a TDVP integration scheme applied to the constrained PXP model.
Both methods evolve identical initial conditions parameterized by angular coordinates (θ₁, θ₃) on the manifold of variational
product states. The TDVP trajectory traces the local variational dynamics, while ScarFinder iteratively identifies the stable
periodic orbit corresponding to the scar trajectory. The coordinates of the resulting trajectories are sampled at discrete
iteration steps to form the Poincaré sections shown in Fig. 6.

Simulations were performed using Julia 1.10 on the Aire HPC cluster at the University of Leeds.
