This is supporting data for "Quantum Many-Body Scars beyond the PXP Model in Rydberg Simulators". DOI: https://doi.org/10.1103/PhysRevLett.134.160401 DOI: https://doi.org/10.48550/arXiv.2410.18913 The data is provided under CC BY-NC 4.0 license. This contains all the data plotted in the main text and Supplemental Online Material (SOM) as well as code (in the form of Python Jupyther notebooks) to reproduce these plots. The data and code are found in the file zip file "Data+Code.zip", which contains two folders names "Data" and "Code". The data is found in the folder "Data" in numpy compressed format (npz) files. Python code to load the data and plot all figures is found in the folder "Code", with one Jupyter notebook per figure. There is also a Python file called custom_funcs.py which contains a few functions shared between different notebooks. Crucially, it contains the function "get_dirp" which returns the relative path from the Code fodler to the Data folder. If you want to modify where the Data and Code folders are relative to each other you will need to modify this function accordingly. The code used to produce the data is available upon reasonable request to the corresponding author. Content of files: PPXPP_K4_OBC_obs_N20.npz : data for quenches with K=4 in the PPXPP model with OBC and 20 sites t_vec: 1D array, time data res_n: 3D array with occupation density after a quench, axis 0 is initial state, axis 1 is physical site, axis 2 is time res_B1: 2D array with expectation value of projector on Bell pair on sites 8 and 9 (starting from 0) after a quench, axis 0 is initial state, axis 1 is time res_B2: 2D array with expectation value of projector on Bell pair on sites 10 and 11 (starting from 0) after a quench, axis 0 is initial state, axis 1 is time initial state 0 is K=4 state, initial state 1 is Y ground state GSy, initial state 2 is Z_4 state (00010001...0001) PPXPP_K4_TDVP_ents.npz: TDVP entanglement entropy data for PPXPP with 4-site unit cell after a quench from the K=4 state t_vec: 1D array, time data ents: 2D array, von Neumann entanglement entropy across the 4 possible cuts (along axis 1) over time (along axis 0) PPXPP_K4_TEBD_OBC_N120.npz: TEBD data for quenches in the PPXPP model with 120 sites and OBC time_64: 1D array, time data for bond-dimension 64 quench from K=4 state energy_64: 2D array, energy density per site (along axis 1) over time (along axis 0) after quench from K=4 state with bond-dimension 64 n_64: 2D array, occupation density per site (along axis 1) over time (along axis 0) after quench from K=4 state with bond-dimension 64 entanglement_64: 2D array, entanglement entropy per bond (along axis 1) over time (along axis 0) after quench from K=4 state with bond-dimension 64 sv_64: 2D array, singular values (square root of entanglement spectrum) across middle bond over time (along axis 0) after quench from K=4 state with bond-dimension 64 time_128: 1D array, time data for bond-dimension 128 quench from K=4 state energy_128: 2D array, energy density per site (along axis 1) over time (along axis 0) after quench from K=4 state with bond-dimension 128 n_128: 2D array, occupation density per site (along axis 1) over time (along axis 0) after quench from K=4 state with bond-dimension 128 entanglement_128: 2D array, entanglement entropy per bond (along axis 1) over time (along axis 0) after quench from K=4 state with bond-dimension 128 sv_128: 2D array, singular values (square root of entanglement spectrum) across middle bond over time (along axis 0) after quench from K=4 state with bond-dimension 128 time_256: 1D array, time data for bond-dimension 256 quench from K=4 state energy_256: 2D array, energy density per site (along axis 1) over time (along axis 0) after quench from K=4 state with bond-dimension 256 n_256: 2D array, occupation density per site (along axis 1) over time (along axis 0) after quench from K=4 state with bond-dimension 256 entanglement_256: 2D array, entanglement entropy per bond (along axis 1) over time (along axis 0) after quench from K=4 state with bond-dimension 256 sv_256: 2D array, singular values (square root of entanglement spectrum) across middle bond over time (along axis 0) after quench from K=4 state with bond-dimension 256 Z4_time_256: 1D array, time data for bond-dimension 256 quench from Z_4 state Z4_energy_256: 2D array, energy density per site (along axis 1) over time (along axis 0) after quench from Z_4 state with bond-dimension 256 Z4_n_256: 2D array, occupation density per site (along axis 1) over time (along axis 0) after quench from Z_4 state with bond-dimension 256 Z4_entanglement_256: 2D array, entanglement entropy per bond (along axis 1) over time (along axis 0) after quench from Z_4 state with bond-dimension 256 Z4_sv_256: 2D array, singular values (square root of entanglement spectrum) across middle bond over time (along axis 0) after quench from Z_4 state with bond-dimension 256 PXP_dyn_Z3_Z4_N24.npz: data for quenches from states with period 3 and 4 in the PXP model with N=24 t_vec: 1D array, time data for all quenches res_fid3: 2D array, fidelity after quenches from the optimally-reviving period 3 state (slice [0,:]) and from the Z_3 state (slice [1,:]), time is along axis 1 res_fid4: 2D array, fidelity after quenches from the K=4 state (slice [0,:]) and from the Z_4 state (slice [1,:]), time is along axis 1 olap3: overlap between the optimally-reviving period 3 state and the Z_3 state olap4: overlap between the K=4 state and the Z_4 state The optimally-reviving period 3 state is defined by angles theta*=[0, 0.1162*Pi, Pi/2] in the MPS manifold PXP_GSZ_GSY_comp_N24.npz: data comparing the properties of the Z ground state GSz (equal to the Z2 state) and the Y ground state GSy in the PXP model with N=24 Hk: 1D array, energy eigenvalues in the relevant symmetry sectors olapZ: 1D array, overlap of GSz with eigenstates olapY: 1D array, overlap of GSy with eigenstates t_vec: 1D array, time data for both quenches fidZ: 1D array, fidelity after a quench from GSz fidY: 1D array, fidelity after a quench from GSy res_SZ: 1D array, half-chain von Neumann entanglement entropy after a quench from GSz res_SY: 1D array, half-chain von Neumann entanglement entropy after a quench from GSy PXP_K4_TDVP_ents.npz: data for TDVP entanglement entropy for PXP with 4-site unit cell after a quench from the K=4 state t_vec: 1D array, time data ents: 2D array, von Neumann entanglement entropy across the 4 possible cuts (along axis 1) over time (along axis 0) PXP_K4_TDVP_traj.npz: data for TDVP angles for PXP with 4-site unit cell after a quench from K=4 state angs: 2D array, angles theta_1 to theta_4 (along axis 1) during evolution of 10000 time-steps (along axis 0) PXP_K4_TDVP_traj_pert.npz: data for TDVP angles for PXP with 4-site unit cell after a quench from parameters near K=4 state angs: 2D array, angles theta_1 to theta_4 (along axis 1) during evolution of 10000 time-steps (along axis 0) PXP_LR_ED2_all_R*_K*_N*.npz: ED data on eigenstates and quench dynamics from special states for the model with PBC and with blockade radius R, unit-cell K, and N sites N: number of sites R: blockade radius K: unit-cell size M: number of unit-cells M2: number of unit-cells after which the first cut is taken for entanglement entropy data labl: list, contains strings indicating the states (in order) used as initial states for quenches and also to compute overlap Hk: 1D array, energy eigenvalues in the relevant symmetry sectors eig_S: 1D array, von Neumann entanglement entropy of eigenstates olap: 2D array, overlap of eigenstates (along axis 0) with states in labl (along axis 1) kp_list: 2D array, list of sectors for momentum-resolved eigenstates, first column is momentum, second column is inversion symmetry (0 when not resolvable at the same time as momentum) kp_lim: 1D array, indices that denote the boundaries of the different symmetry sectors in Hk and olap for momentum-resolved eigenstates DZ: norm of the difference between Hz=[H,Hy]/2i and the analytical Ansatz for Hz t_vec: 1D array, time data, shared for all quenches res_HZ: 2D array, expectation value of Hz operator after a quench for all initial states (along axis 0) over time (along axis 1) res_HY: 2D array, expectation value of Hy operator after a quench for all initial states (along axis 0) over time (along axis 1) res_n: 3D array, expectation value of the number of excitations on each of the K sublattices (along axis 1), after a quench from all initial states in labl (along axis 0) over time (along axis 2) res_rc: 2D array, expectation value of the difference between the commutator [Hz,H] and Hy after a quench from all initial states in labl (along axis 0) over time (along axis 1) res_fid: 3D array, overlap between the time evolved initial states in labl after a quench (along axis 0) and all states of interest (along axis 1) over time (along axis 2). The first "states of interest" are simply the states in labl, while the last two are the Y ceiling state CSy and the Z ceiling state CSz res_n: 3D array, entanglement entropy along the K different bipartite cuts that maximise subsystem size while cutting at the same place in the two unit-cells (along axis 1), after a quench from all initial states in labl (along axis 0) over time (along axis 2) opti_fZ: overlap between the Z ground state GSz and the numerically-optimized state in the MPS manifold with the highest overlap with it opti_xZ: angles (!!! in units of Pi !!!) defining the numerically-optimized state in the MPS manifold with the highest overlap with the Z ground state GSz opti_fY: overlap between the Y ground state GSy and the numerically-optimized state in the MPS manifold with the highest overlap with it opti_xY: angles (!!! in units of Pi !!!) defining the numerically-optimized state in the MPS manifold with the highest overlap with the Y ground state GSy beta: relative weight of the state with an excitation on the middle site in the K state. Meaningful only for odd values of K. Kf: overlap between the Z ground state GSz and the K state with maximum overlap with it. For even K the latter is just the K state, for odd K this is numerically optimized over the value of beta. Kx: value of beta for which the resulting K state has maximum overlap with the Z ground state GSz. The optimally-reviving states were found numerically as the best reviving state in the relevant MPS manifold. They are defined from the following angles in their respective manifold PXP, R=1: K=2: [0.5, 0.5]*Pi K=3: [0, 0.1162, 0.5]*Pi K=4: [0,0,0.25,0.5]*Pi PPXPP, R=2: K=3: [0.5, 0.5, 0.5]*Pi K=4: [0, 0, 0.25, 0.5]*Pi K=5: [0, 0, 0.12662446, 0.25, 0.5]*Pi K=6: [0.14825963, 0.84778737, 0.15221256, 0.14825964, 0.15221242, 0.15221243]*Pi PPPXPPP, R=2: K=4: [0.5, 0.5, 0.5, 0.5]*Pi K=5: [0, 0.09094787, 0.67621579, 0.38364001, 0.5]*Pi K=6: [0, 0, 0.1869617, 0.27980698, 0.44241983, 0.5]*Pi K=7: [0, 0, 0, 0.06448484, 0.20172055, 0.26645423, 0.5]*Pi PXP_LR_ED_rand2_R*_K*_N*.npz: ED data on eigenstates and quench dynamics from 100 random states (projected to have period K) for the model with PBC and with blockade radius R, unit-cell K, and N sites N: number of sites R: blockade radius K: unit-cell size M: number of unit-cells M2: number of unit-cells after which the first cut is taken for entanglement entropy data Hk: 1D array, energy eigenvalues in the symmetry sectors relevant for states with period K olap: 2D array, overlap of eigenstates (along axis 0) with initial states (along axis 1) kp_list: 2D array, list of sectors for momentum-resolved eigenstates, first column is momentum, second column is inversion symmetry (0 when not resolvable at the same time as momentum) kp_lim: 1D array, indices that denote the boundaries of the different symmetry sectors in Hk and olap for momentum-resolved eigenstates t_vec: 1D array, time data, shared for all quenches res_HZ: 2D array, expectation value of Hz operator after a quench for all initial states (along axis 0) over time (along axis 1) res_HY: 2D array, expectation value of Hy operator after a quench for all initial states (along axis 0) over time (along axis 1) res_rc: 2D array, expectation value of the difference between the commutator [Hz,H] and Hy after a quench from all initial states (along axis 0) over time (along axis 1) res_fid: 2D array, fidelity after a quench from all initial states (along axis 0) over time (along axis 1) pstates: 2D array, binary representation of all initial states, before they are projected into the relevant symmetry sectors to ensure they have period K PXP_LR_eigs_kP_R2_K5_N25.npz: eigenstate data for PPXPP with K=5 and N=25 Hk: 1D array, energies of eigenstates olap: overlap of momentum-resolved eigenstates with K=5 state kp_list: 2D array, list of sectors for momentum-resolved eigenstates, first column is momentum, second column is inversion symmetry (0 when not resolvable at the same time as momentum) kp_lim: 1D array, indices that denote the boundaries of the different symmetry sectors in Hk and olap for momentum-resolved eigenstates olapP: overlap of inversion symmetry-resolved eigenstates with K=5 state kp_listP: 2D array, list of sectors for inversion-symmetry-resolved eigenstates, first column is absolute value of momentum, second column is inversion symmetry kp_limP: 1D array, indices that denote the boundaries of the different symmetry sectors in Hk and olapP for inversion-symmetry-resolved eigenstates PXP_LR_init_comp_R1_K3_N18.npz: data to compare the trajectories of different initial state for PXP with K=3 and N=18 t_vec: 1D array, time data res_fid: 3D array, axis 0 is the initial state of the quench, axis 1 is the state with which the overlap on the time evolved-state is computed, axis 2 is time In axes 0 and 1 of res_fid, the states are the following: 0: Y ground state GSY 1: Y ceiling state CSY 2: Z ground state GSZ 3: Z ceiling state CSZ 4: optimally-reviving period 3 state defined by angles theta*=[0, 0.1162*Pi, Pi/2] in the MPS manifold Rydberg_PPXPP_K4_N20_V18_d0.400.npz : data for quenches with K=4 in the PPXPP regime of the full Rydberg model with OBC and 20 sites V1: nearest-neighbor interaction value in MHz*2*Pi Omeg: Rabi frequency in MHz*2*Pi N: number of sites nbs: number of states in Hilbert space nbPPXPP: number of states respecting the PPXPP constraint avV: 1D array, total van der Waals interaction felt by each atom due to all of its neighbor dopt: correction factor to use with respect to the theoretical detuning needed to cancel the total van der Waals interaction on the middle site t_vec: 1D array, time data in 2*Pi*microseconds B1_idx: 1D array, sites (starting from 0) where Bell-pair projection is computed on to get res_B1 B2_idx: 1D array, sites (starting from 0) where Bell-pair projection is computed on to get res_B2 res_B1: 2D array with expectation value of projector on Bell pair on sites B1_idx (starting from 0) after a quench, axis 0 is initial state, axis 1 is time res_B2: 2D array with expectation value of projector on Bell pair on sites B2_idx (starting from 0) after a quench, axis 0 is initial state, axis 1 is time res_n: 3D array with occupation density after a quench, axis 0 is initial state, axis 1 is physical site, axis 2 is time res_fid: 2D array with fidelity after a quench, axis 0 is initial state, axis 1 is time res_proj: 2D array with expectation value of projector on PPXPP subspace after a quench, axis 0 is initial state, axis 1 is time initial state 0 is K=4 state, initial state 1 is Y ground state, initial state 2 is Z_4 state (00010001...0001)