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

Title: Dataset for Figure 7(b,c) – Comparison of entanglement and fidelity dynamics between TDVP and ScarFinder states

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 (b) and (c) of Figure 7 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).

Panels (b,c) compare the bipartite entanglement entropy and fidelity dynamics obtained from optimized scar
initial states identified via two independent methods: the TDVP Poincaré-section approach (blue) and the
ScarFinder algorithm (orange).

  - Panel (b): Entanglement entropy S_{L/2}(t) dynamics for the two optimized initial states.
  - Panel (c): Fidelity revival dynamics N[ψ₀, ψ_t] for the same pair of states, showing that the ScarFinder-optimized
    trajectory exhibits slightly enhanced revivals compared to TDVP.

Cite as: Ren, Jie (2025): Dataset for Figure 7(b,c) – Comparison of entanglement and fidelity dynamics between TDVP and ScarFinder states.
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:
S0.dat – Entanglement entropy S_{L/2}(t) for the TDVP-optimized state (blue curve, Fig. 7b).
S1.dat – Entanglement entropy S_{L/2}(t) for the ScarFinder-optimized state (orange curve, Fig. 7b).
F0.dat – Fidelity N[ψ₀, ψ_t] for the TDVP-optimized state (blue curve, Fig. 7c).
F1.dat – Fidelity N[ψ₀, ψ_t] for the ScarFinder-optimized state (orange curve, Fig. 7c).

Each file contains two columns corresponding to (time, observable value).
All data are stored as plain-text numerical arrays compatible with standard analysis tools (Python, Julia, MATLAB, etc.).


5. METHODS
----------
The optimized scar states were obtained using two distinct procedures: (1) the TDVP Poincaré-section optimization and
(2) the ScarFinder fixed-point algorithm. Both were applied to the PXP Hamiltonian with a three-site unit cell.
Subsequent time evolution was performed using the iTEBD algorithm with a fixed time step Δt = 0.2 to evaluate
the entanglement entropy and fidelity revival dynamics over 20 time units. The resulting datasets quantify the
differences in stability and revival strength between the two methods.

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