Data of "Anomalous transport in quasiperiodic lattices: emergent exceptional points at band edges and log-periodic oscillationss"

Data Description for the Figure Scripts The plotting scripts read the CSV data files listed below or calculate simple plotting data directly, and then generate the final PDF figures. The numerical data are generated by the corresponding `HPC_*.jl` scripts. For most datasets, run the same HPC script with different energies and output filenames to obtain all CSV files used in one figure. Fig. 1 Run `MSFig_spectrum.jl` to get Fig.1. This figure is calculated directly in the plotting file. It diagonalizes the finite-size AAH Hamiltonian at the extended phase, constructs the band intervals, rescales selected subbands, and marks representative `E_out`, `E_in`, and `E_edge` points. No external CSV data are used for this figure. Fig. 2 Run `HPC_lnG_ext.jl` to obtain the typical conductance data in the extended regime of the AAH model. The energies `E_in1`, `E_in2`, `E_out1`, and `E_out2` are selected in this file from the spectrum files `data/E/ext/E_k0`, `data/E/ext/E_kpi`, and `data/E/ext/E_kpi2` calculated by `HPC_ed.jl`. Run it with different energies and output filenames to obtain: - `data/AAH_scaling/ext/L_Ein1.csv`, `data/AAH_scaling/ext/lnG_Ein1.csv` - `data/AAH_scaling/ext/L_Ein2.csv`, `data/AAH_scaling/ext/lnG_Ein2.csv` - `data/AAH_scaling/ext/L_Eout1.csv`, `data/AAH_scaling/ext/lnG_Eout1.csv` - `data/AAH_scaling/ext/L_Eout2.csv`, `data/AAH_scaling/ext/lnG_Eout2.csv` - `data/AAH_scaling/ext/L_Eedge1.csv`, `data/AAH_scaling/ext/lnG_Eedge1.csv` - `data/AAH_scaling/ext/L_Eedge2.csv`, `data/AAH_scaling/ext/lnG_Eedge2.csv` Run `HPC_TMeigen.jl` to locate the edge energies and to obtain the transfer-matrix trace scans: - `data/AAH_scaling/ext/E_arr1.csv`, `data/AAH_scaling/ext/trM1.csv` - `data/AAH_scaling/ext/E_arr2.csv`, `data/AAH_scaling/ext/trM2.csv` Run `HPC_TM12.jl` to obtain the transfer-matrix element data at the two edge energies: - `data/AAH_scaling/ext/T12L_edge1.csv`, `data/AAH_scaling/ext/T12_edge1.csv` - `data/AAH_scaling/ext/T12L_edge2.csv`, `data/AAH_scaling/ext/T12_edge2.csv` Run `MSFig_lnG_ext.jl` to get Fig.2. Panel (a) uses the `E_in` conductance data. Panel (b) uses the `E_out` conductance data. Panel (c) uses the `E_edge` conductance data. Panel (d) uses the `T12` data, and its insets use the trace-scan data from `HPC_TMeigen.jl`. Fig. 3 Run `HPC_lnG_loc.jl` to obtain the typical conductance data in the localized regime of the AAH model. The selected energies are defined in this file from the spectrum files `data/E/loc/E_k0`, `data/E/loc/E_kpi`, and `data/E/loc/E_kpi2` given by `HPC_ed.jl`. Run it with different energies and output filenames to obtain: - `data/AAH_scaling/loc/L_Ein1.csv`, `data/AAH_scaling/loc/lnG_Ein1.csv` - `data/AAH_scaling/loc/L_Ein2.csv`, `data/AAH_scaling/loc/lnG_Ein2.csv` - `data/AAH_scaling/loc/L_Eout1.csv`, `data/AAH_scaling/loc/lnG_Eout1.csv` - `data/AAH_scaling/loc/L_Eout2.csv`, `data/AAH_scaling/loc/lnG_Eout2.csv` Run `MSFig_lnG_loc.jl` to get Fig.3. Panel (a) uses the two `E_in` datasets. Panel (b) uses the two `E_out` datasets. Fig. 4 Run `HPC_ed.jl` to obtain the AAH critical-regime spectrum files used for energy selection: - `data/E/crit/E_k0` - `data/E/crit/E_kpi` - `data/E/crit/E_kpi2` Run `HPC_lnG_crit.jl` to obtain the typical conductance data at four selected critical energies. Run this file with different energies and output filenames to obtain: - `data/AAH_scaling/crit/L_Ein1.csv`, `data/AAH_scaling/crit/lnG_Ein1.csv` - `data/AAH_scaling/crit/L_Ein2.csv`, `data/AAH_scaling/crit/lnG_Ein2.csv` - `data/AAH_scaling/crit/L_Ein3.csv`, `data/AAH_scaling/crit/lnG_Ein3.csv` - `data/AAH_scaling/crit/L_Ein4.csv`, `data/AAH_scaling/crit/lnG_Ein4.csv` Run `MSFig_lnG_crit.jl` to get Fig.4. Panels (a), (b), (c), and (d) use the datasets for `E_in1`, `E_in3`, `E_in4`, and `E_in2`, respectively. Fig. 5 Run `HPC_ed.jl` to obtain the AAH critical-regime spectrum files used for energy selection. Run `HPC_lnG_crit.jl` to obtain the conductance data: - `data/AAH_scaling/crit/L_Ein1.csv`, `data/AAH_scaling/crit/lnG_Ein1.csv` - `data/AAH_scaling/crit/L_Eout1.csv`, `data/AAH_scaling/crit/lnG_Eout1.csv` - `data/AAH_scaling/crit/L_Eout2.csv`, `data/AAH_scaling/crit/lnG_Eout2.csv` These files contain the typical conductance at one in-band critical energy and two outside/gap energies. Run `HPC_lnG_crit.jl` with different energies and output filenames to get all three datasets. Run `MSFig_lnG_crit_smooth.jl` to get Fig.5. Panel (a) uses the `E_in1` data. Panel (b) uses the `E_out1` and `E_out2` data. Fig. 6 Run `HPC_GAAH_spec.jl` with different values of `V` to obtain the GAAH spectrum data used in panel (a): - `data/GAAH_scaling/crit/Lyap_Ec/gap_scaling/spec/EV1.csv` through `data/GAAH_scaling/crit/Lyap_Ec/gap_scaling/spec/EV401.csv` Run `HPC_lyap_Ec.jl` to obtain the Lyapunov exponents at the selected mobility-edge energies: - `data/GAAH_scaling/crit/lyap_Ec1.csv` - `data/GAAH_scaling/crit/lyap_Ec2.csv` - `data/GAAH_scaling/crit/lyap_Ec3.csv` Run `HPC_GAAH_lnG_crit.jl` to obtain the typical conductance data at the three mobility-edge energies. Run this file with different parameters and output filenames to obtain: - `data/GAAH_scaling/crit/L_Ec1.csv`, `data/GAAH_scaling/crit/lnG_Ec1.csv` - `data/GAAH_scaling/crit/L_Ec2.csv`, `data/GAAH_scaling/crit/lnG_Ec2.csv` - `data/GAAH_scaling/crit/L_Ec3.csv`, `data/GAAH_scaling/crit/lnG_Ec3.csv` Run `HPC_GAAH_gap.jl` to obtain the gap-scaling data near the three mobility-edge energies: - `data/GAAH_scaling/crit/Lyap_Ec/gap_scaling/L_Ec1.csv`, `data/GAAH_scaling/crit/Lyap_Ec/gap_scaling/lngap_Ec1.csv` - `data/GAAH_scaling/crit/Lyap_Ec/gap_scaling/L_Ec2.csv`, `data/GAAH_scaling/crit/Lyap_Ec/gap_scaling/lngap_Ec2.csv` - `data/GAAH_scaling/crit/Lyap_Ec/gap_scaling/L_Ec3.csv`, `data/GAAH_scaling/crit/Lyap_Ec/gap_scaling/lngap_Ec3.csv` Run `MSFig_GAAH_lnG_ME.jl` to get Fig.6. Panel (a) uses the spectrum data. Panel (b) uses the mobility-edge conductance data. The inset of panel (b) uses the gap-scaling data. Fig. 7 Run `HPC_GAAH_lnG_ext_loc.jl` to obtain the typical conductance data in the GAAH model with both extended and localized in-band energies. The energies are selected in this file from the spectrum files `data/GAAH_E/E_k0`, `data/GAAH_E/E_kpi`, and `data/GAAH_E/E_kpi2` calculated by `HPC_ed.jl`. Run this file with different energies and output filenames to obtain: - `data/GAAH_scaling/ext_loc/L_Eext_in1.csv`, `data/GAAH_scaling/ext_loc/lnG_Eext_in1.csv` - `data/GAAH_scaling/ext_loc/L_Eext_in2.csv`, `data/GAAH_scaling/ext_loc/lnG_Eext_in2.csv` - `data/GAAH_scaling/ext_loc/L_Eedge1.csv`, `data/GAAH_scaling/ext_loc/lnG_Eedge1.csv` - `data/GAAH_scaling/ext_loc/L_Eedge2.csv`, `data/GAAH_scaling/ext_loc/lnG_Eedge2.csv` - `data/GAAH_scaling/ext_loc/L_Eloc_in1.csv`, `data/GAAH_scaling/ext_loc/lnG_Eloc_in1.csv` - `data/GAAH_scaling/ext_loc/L_Eloc_in2.csv`, `data/GAAH_scaling/ext_loc/lnG_Eloc_in2.csv` - `data/GAAH_scaling/ext_loc/L_Eout1.csv`, `data/GAAH_scaling/ext_loc/lnG_Eout1.csv` - `data/GAAH_scaling/ext_loc/L_Eout2.csv`, `data/GAAH_scaling/ext_loc/lnG_Eout2.csv` Run `HPC_ext_Eedge_lyap.jl` for the Lyapunov/edge-energy check used when choosing the edge energies. Run `MSFig_GAAH_lnG_ext_loc.jl` to get Fig.7. Panel (a) uses the extended in-band datasets. Panel (b) uses the edge-energy datasets. Panel (c) uses the localized in-band datasets. Panel (d) uses the outside/gap datasets.