Thermodynamic stability at the two-particle level - numerical results for the two-orbital hubbard model

doi:doi:10.58160/PCGsCFdwLYjyIEDv

Thermodynamic stability at the two-particle level - numerical results for the two-orbital hubbard model

Abstract: This dataset contains the DMFT/QMC results for the example of the two-orbital Hubbard model shown in the article "Thermodynamic Stability at the Two-Particle Level". It contains parameters, one-particle Green's functions, and observables in w2dynamics output format as well as patches for relevant functionality not contained in current versions of w2dynamics at the time of publication and scripts used for post-processing of the data and the creation of some of the graphs. For size reasons, the data files containing the corresponding two-particle Green's functions are split into multiple subdatasets whose identifiers are listed above. TechnicalRemarks: The data files are contained in directories named beta35 and beta50 for the inverse temperature used in the respective calculations, with files containing the two-particle Green's functions contained in the subdatasets listed above and indicated by names containing 'G2'. All calculations were performed for two-orbital Hubbard models on a Bethe lattice with density-density interaction with fixed ratios between the interaction coefficients. The individual file names contain the inverse temperature, e.g. 'b35' for beta=35, Hubbard-U interaction strength, e.g. 'U1.44' for U=1.44, and usually the chemical potential μ, e.g. 'mu1.26000' for μ=1.26. The file name segment 'ma...' present in some file names redundantly gives the difference of the used chemical potential from that necessary for half-filling. In the coexistence region, the phase of the solution depends on the procedure which is indicated by the name segment 'upward' / 'downward' / 'instable' (also sometimes shortened to just the initial letter) indicating the insulating or strongly correlated metallic phase, the weakly correlated metallic phase, and the unstable phase respectively. For some of the files containing unstable solutions, the targeted value of the quasiparticle weight Z calculated from the self-energy value at the first Matsubara frequency is given in the 'Ztarget...' segment instead of an approximate value of the chemical potential (which is not preset as a fixed parameter for calculating unstable solutions). File names of files containing two-particle Green's functions additionally contain 's...' indicating separate calculations differing only in the used PRNG seed that allow further statistical post-processing beyond that done automatically by w2dynamics. n(mu) plots as shown in Figs. 2 and 3 of the article can be created using the script 'kappa_2band_create_mu_n_plot.py' by calling it with the appropriate arguments, e.g. using commands like python kappa_2band_create_mu_n_plot.py -r "kappa_2band_bethe_dens_b35_U([0-9.]*)_([muZtarget0-9.]*).*hdf.*" --axisgroup 1 -k '$U/D = {grp[0]}$' --imsiwsort --nmin 2.0 --nmax 2.08 --mumin 0.0 --mumax 0.15 --nmu --onecolsize *.hdf5.zst in the beta35 directory to create a plot like in Fig. 2 and python kappa_2band_create_mu_n_plot.py -r "kappa_2band_bethe_dens_b50_U([0-9.]*)_([muZtarget0-9.]*).*hdf.*" --axisgroup 1 -k '$U/D = {grp[0]}$' --imsiwsort --nmin 2.0 --nmax 2.14 --mumin 0.0 --mumax 0.22 --nmu --onecolsize *.hdf5.zst in the beta50 directory to create a plot like in Fig. 3. The script 'chi_d_orblt_diagonalize.py' can be used to compute and diagonalize the generalized susceptibility by passing a data file with the one-particle Green's function as argument after '--onepfile' and one with the corresponding two-particle Green's function after '--twopfile'. From the created .npz files, a plot like in Fig. 1 of the supplemental material can be created using the script 'chi_eigenbasis_multi_barcontribs.py' by calling it with the appropriate arguments, e.g. python chi_eigenbasis_multi_barcontribs.py --force-centrosymm-contribs --onecolsize --bargraph 2 --beta 50 --hopping 0.5 --contrib real --barorder contrib kappa_2band_bethe_dens_b50_U1.4910_mu1.4924_u_chi_orblt.npz kappa_2band_bethe_dens_b50_U1.4915_mu1.4937_u_chi_orblt.npz kappa_2band_bethe_dens_b50_U1.4920_mu1.49510_u_chi_orblt.npz kappa_2band_bethe_dens_b50_U1.4930_mu1.49780_u_chi_orblt.npz kappa_2band_bethe_dens_b50_U1.50_mu1.51740_u_chi_orblt.npz --tickstrings '$U/D = 1.4910$' '$U/D = 1.4915$' '$U/D = 1.4920$' '$U/D = 1.4930$' '$U/D = 1.5000$' to create a similar plot showing the same data after the listed .npz files with the generalized susceptibility data have been created. Patches in the patch directory can be applied to w2dynamics 1.1.5 as published on GitHub to add functionality that allows performing calculations converging toward unstable solutions like those contained in this data set. This information is also contained in the markdown-formatted file README.md contained in the datasets. Other: We are grateful for funding support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project ID 390858490) as well as through the Collaborative Research Center SFB 1170 ToCoTronics (Project ID 258499086).

BibTex:

@dataset{Kowalski_Alexander_2024,
    abstract = {Abstract: This dataset contains the DMFT/QMC results for the example of the two-orbital Hubbard model shown in the article "Thermodynamic Stability at the Two-Particle Level". It contains parameters, one-particle Green's functions, and observables in w2dynamics output format as well as patches for relevant functionality not contained in current versions of w2dynamics at the time of publication and scripts used for post-processing of the data and the creation of some of the graphs. For size reasons, the data files containing the corresponding two-particle Green's functions are split into multiple subdatasets whose identifiers are listed above.
TechnicalRemarks: The data files are contained in directories named beta35 and beta50 for the inverse temperature used in the respective calculations, with files containing the two-particle Green's functions contained in the subdatasets listed above and indicated by names containing 'G2'. All calculations were performed for two-orbital Hubbard models on a Bethe lattice with density-density interaction with fixed ratios between the interaction coefficients. The individual file names contain the inverse temperature, e.g. '_b35_' for beta=35, Hubbard-U interaction strength, e.g. '_U1.44_' for U=1.44, and usually the chemical potential μ, e.g. '_mu1.26000_' for μ=1.26. The file name segment '_ma..._' present in some file names redundantly gives the difference of the used chemical potential from that necessary for half-filling. In the coexistence region, the phase of the solution depends on the procedure which is indicated by the name segment 'upward' / 'downward' / 'instable' (also sometimes shortened to just the initial letter) indicating the insulating or strongly correlated metallic phase, the weakly correlated metallic phase, and the unstable phase respectively. For some of the files containing unstable solutions, the targeted value of the quasiparticle weight Z calculated from the self-energy value at the first Matsubara frequency is given in the '_Ztarget..._' segment instead of an approximate value of the chemical potential (which is not preset as a fixed parameter for calculating unstable solutions). File names of files containing two-particle Green's functions additionally contain '_s..._' indicating separate calculations differing only in the used PRNG seed that allow further statistical post-processing beyond that done automatically by w2dynamics.  n(mu) plots as shown in Figs. 2 and 3 of the article can be created using the script 'kappa_2band_create_mu_n_plot.py' by calling it with the appropriate arguments, e.g. using commands like `python kappa_2band_create_mu_n_plot.py -r "kappa_2band_bethe_dens_b35_U([0-9.]*)_([muZtarget0-9.]*).*hdf.*" --axisgroup 1 -k '$U/D = {grp[0]}$' --imsiwsort --nmin 2.0 --nmax 2.08 --mumin 0.0 --mumax 0.15 --nmu --onecolsize *.hdf5.zst` in the beta35 directory to create a plot like in Fig. 2 and `python kappa_2band_create_mu_n_plot.py -r "kappa_2band_bethe_dens_b50_U([0-9.]*)_([muZtarget0-9.]*).*hdf.*" --axisgroup 1 -k '$U/D = {grp[0]}$' --imsiwsort --nmin 2.0 --nmax 2.14 --mumin 0.0 --mumax 0.22 --nmu --onecolsize *.hdf5.zst` in the beta50 directory to create a plot like in Fig. 3. The script 'chi_d_orblt_diagonalize.py' can be used to compute and diagonalize the generalized susceptibility by passing a data file with the one-particle Green's function as argument after '--onepfile' and one with the corresponding two-particle Green's function after '--twopfile'.  From the created .npz files, a plot like in Fig. 1 of the supplemental material can be created using the script 'chi_eigenbasis_multi_barcontribs.py' by calling it with the appropriate arguments, e.g. `python chi_eigenbasis_multi_barcontribs.py --force-centrosymm-contribs --onecolsize --bargraph 2 --beta 50 --hopping 0.5 --contrib real --barorder contrib kappa_2band_bethe_dens_b50_U1.4910_mu1.4924_u_chi_orblt.npz kappa_2band_bethe_dens_b50_U1.4915_mu1.4937_u_chi_orblt.npz kappa_2band_bethe_dens_b50_U1.4920_mu1.49510_u_chi_orblt.npz kappa_2band_bethe_dens_b50_U1.4930_mu1.49780_u_chi_orblt.npz kappa_2band_bethe_dens_b50_U1.50_mu1.51740_u_chi_orblt.npz  --tickstrings '$U/D = 1.4910$' '$U/D = 1.4915$' '$U/D = 1.4920$' '$U/D = 1.4930$' '$U/D = 1.5000$'` to create a similar plot showing the same data after the listed .npz files with the generalized susceptibility data have been created. Patches in the patch directory can be applied to w2dynamics 1.1.5 as published on GitHub to add functionality that allows performing calculations converging toward unstable solutions like those contained in this data set. This information is also contained in the markdown-formatted file README.md contained in the datasets.
Other: We are grateful for funding support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat (EXC 2147, Project ID 390858490) as well as through the Collaborative Research Center SFB 1170 ToCoTronics (Project ID 258499086).},
    author = {Kowalski, Alexander},
    doi = {10.58160/PCGsCFdwLYjyIEDv},
    institution = {RADAR},
    keyword = {'Continuous-time quantum Monte Carlo', 'Dynamische Molekularfeldtheorie', 'Hubbard-Modell', 'Kondensierte Materie', 'Metal-insulator transitions', 'Metall-Isolator-Phasenumwandlung', 'Monte-Carlo-Simulation', 'Phase separation', 'Starke Kopplung', 'Strongly correlated electron systems', 'Thermodynamic stability'},
    title = {Thermodynamic stability at the two-particle level - numerical results for the two-orbital hubbard model},
    url = {https://service.tib.eu/ldmservice/vdataset/rdr-doi-10-58160-pcgscfdwlyjyiedv},
    year = {2024}
}