This data repository contains the original figures, numerical (raw) data, scripts that were used to calculate this data, and plot scripts to reproduce the figures from the publication "Origin of misleading convergence in self-consistent many-electron theories: Fundamental aspects and practical implications" at Physical Review Letters. The preprint is available on arXiv where also the LaTeX source files can be found.
For the Python scripts, the following non-standard libraries have been used: numpy 1.26., matplotlib 3.10., triqs 3.3.0 with the package CTINT 3.1.0 (branch DEV_NEW_ALPHA_REB).
The structure of the repository is the following:
In the folder "Data" the data that was used for creating the figures of the paper are stored.
In the folder "Scripts" the scripts for creating and plotting the data are stored.
In the folder "Figures" the original figures used in the publication are stored.
The content in Data is the following:
| inv_lr_dmu0_mix1 Data for the G_0^{-1} iteration in the conventional scheme for the HA at ph-symmetry and p=1 (middle lower panel in Fig.2 and lower left panel in Fig.S3 of the SM)
| inv_lr_dmu0_mix05 Data for the G_0^{-1} iteration in the conventional scheme for the HA at ph-symmetry and p=0.5 (middle lower panel in Fig.2 and lower left panel in Fig.S3 of the SM)
| inv_lr_dmu0_mix0p1 Data for the G_0^{-1} iteration in the conventional scheme for the HA at ph-symmetry and p=0.1 (middle lower panel in Fig.2 and lower left panel in Fig.S3 of the SM)
| chi_renorm.npz Data for the first (Pseudo-)Divergence line of \chi_0^{-1}\chi_c in the HA (used for lower left panel of Fig.2)
| stability_phasespace.npz Data for the p-dependent stability regions for the G_0^{-1} iteration in the conventional scheme for the HA (used for lower left panel of Fig.2)
| stay_on_track_inv_dmu0_mix0p1 Data for the G_0^{-1} iteration in the modified scheme for HA at ph-symmetry and p=0.1 (bottom panel in Fig.3)
| stay_on_track_inv_dmu1p5_mix0p1 Data for the G_0^{-1} iteration in the modified scheme for HA at \delta\mu=1.5 and p=0.1 (bottom panel in Fig.S4 of the SM)
| start_phys_stay_inv_dmu0_mix0p1 Data for the G_0^{-1} iteration in the modified scheme for HA at ph-symmetry and p=0.1. As a starting point the physical solution with a slight perturbation is used. (Used for the comparison in Fig.S9 in the SM)
| start_phys_stay_inv_dmu0_mix0p5 Data for the G_0^{-1} iteration in the modified scheme for HA at ph-symmetry and p=0.5. As a starting point the physical solution with a slight perturbation is used. (Used for the comparison in Fig.S10 in the SM)
| lr_stay_inv_dmu0_mix0p5 Data for the G_0^{-1} iteration in the modified scheme for HA at ph-symmetry and p=0.5. As a starting point the converged solution of the previous data point is used. (Used for the comparison in Fig.S8 in the SM)
| start_phys_quasi_newton_dmu0_mix0p1 Data for the G_0^{-1} iteration with the Chord method for HA at ph-symmetry and p=0.1. As a starting point the physical solution with a slight perturbation is used. (Used for the comparison in Fig.S9 in the SM)
| start_phys_quasi_newton_dmu0_mix0p5 Data for the G_0^{-1} iteration with the Chord method for HA at ph-symmetry and p=0.5. As a starting point the physical solution with a slight perturbation is used. (Used for the comparison in Fig.S10 in the SM)
| lr_quasi_newton_dmu0_mix0p5 Data for the G_0^{-1} iteration with the Chord method for HA at ph-symmetry and p=0.5. As a starting point the converged solution of the previous data point is used. (Used for the comparison in Fig.S8 in the SM)
The Data that is computed using the ctint solver of TRIQS is structured as follows:
params.h5 contains parameters of the HA, e.g. U,\beta,\delta\mu, ..., the parameters of the iteration, e.g. maximal iteration, convergence criteria, ..., and the parameters of the ctint solver, e.g. n_cycles, n_warmup_cycles, ...
final.h5 contains the converged quantities (G,G0,Sigma,density) of the iteration for each U value as well the number of iterations needed and if the iteration converged
U%d.h5 contains quantities for a specific U value (determine by %d which is the index in the U array) with the iteration history
The content in Scripts is the following:
| plot_schematic.ipynb Plots the schematic Fig.1.
| HA_misleading_conv_inv.py Computes the G_0^{-1} iteration in the conventional scheme for the HA using the ctint solver of TRIQS. Used to compute inv_lr_dmu0_mix1, inv_lr_dmu0_mix0p5 and inv_lr_dmu0_mix0p1.
| HA_iteration_stay_on_track.py Computes the G_0^{-1} iteration in the modified scheme for the HA using the ctint solver of TRIQS. Used to compute stay_on_track_inv_dmu0_mix0p1, stay_on_track_inv_dmu1p5_mix0p1, start_phys_stay_inv_dmu0_mix0p1, start_phys_stay_inv_dmu0_mix0p5 and lr_stay_inv_dmu0_mix0p5.
| HA_iteration_quasi_Newton.py Computes the G_0^{-1} iteration with the Chord method for the HA using the ctint solver of TRIQS. Used to compute start_phys_quasi_newton_dmu0_mix0p1, start_phys_quasi_newton_dmu0_mix0p5 and lr_quasi_newton_dmu0_mix0p5.
| HA_plot_different_ps.ipynb Plots HA results for the G_0^{-1} iteration in the conventional scheme (bottom panels of Fig.2 in the main text and Fig.S3 of the SM)
| HA_plot_phasespace.ipynb Plots the stability phase space for the G_0^{-1} iteration in the HA (lower left panel of Fig.2)
| HA_Phasespace_Div_const_alpha.ipynb This script is used to compute chi_renorm.npz. It computes the phasespace location of the (pseudo-)divergences of \chi_0^{-1}\chi for the HA where alpha is the ration between magnetic field and chemical potential and therefore is set to 0.
| HA_stability.ipynb This script is used to compute stability_phasespace.npz. It computes the p-dependent stability region of the G_0^{-1} iteration in the conventional scheme for the HA.
| HA_plot_modified_iteration.ipynb Plots HA results for the G_0^{-1} iteration in the modified scheme (bottom panel of Fig.3 in the main text and Fig.S4 of the SM)
| HA_compare_modifed_chord.ipynb Plots a comparison between the modified scheme and the Chord method (Fig.S8, Fig.S9 and Fig.S10 in the SM)
| HA.py Contains the analytical expressions for the generalized susceptibilities and Green's function in the Hubbard Atom
| ZP_conventional_iteration.ipynb Computes and plots the results for the G_0^{-1} iteration in the conventional scheme in the ZP model (upper panels of Fig.2 in the main text and Fig.S3 of the SM). Further it plots the weak and strong coupling fixed point of the G_0^{-1} iteration in the ZP model (Fig.S2 in the SM).
| ZP_plot_phasespace.ipynb Plots the stability phase space for the G_0^{-1} iteration in the ZP model (upper left panel of Fig.2)
| ZP_stay_on_track_g0.ipynb Computes and plots the results for the G_0^{-1} iteration in the modified scheme in the ZP model (upper panel of Fig.3 in the main text and Fig.S4 of the SM).
| ZP_Flow_diagram.ipynb Computes and plots the flow-digram in the complex plane of G_0^{-1} for the conventional and the modified scheme for iteration in G_0^{-1} in the ZP model (middle panel of Fig.3 in the main text and Fig.S4 of the SM).
| ZP_G_iteration.ipynb Computes and plots the results for the G^{-1} iteration in the conventional and the modified scheme for the ZP model (Fig.4 in the main text and Fig.S5, Fig.S6 and Fig.S7 of the SM).
| zp.py Contains the analytical expressions for the generalized susceptibilities and Green's function in the zero point model
| compare_ZP_and_BM.ipynb Computes and compares the Green's function of the ZP model and the binary mixture model (Fig.S1 in the SM).
| bm.py Contains the analytical expressions for the generalized susceptibilities and Green's function in the binary mixture model