Data for: "Waterfalls: umbilical cords at the birth of Hubbard bands"

Context and methodology

• This repository contains raw data from the associated research work. It serves the purpose of aiding interested readers to reproduce the results of the related work and verify their validity.
• The research area in which this dataset is created is that of condensed matter, strongly correlated electron systems, ARPES, cuprates, and nickelates.
• This dataset was created using the w2dynamics code for DMFT calculations, the ana_cont package for analytic continuation, and the DGApy code for DGA calculations. 

Technical details

• For each figure there is a corresponding folder in data folder containing the data shown in the figure. Data files are of type hk, hdf5, npz, and txt and named logically after data they contain.
• Reading the data requires python (version 3.10.13, numpy version 1.26.0) with h5py (version 3.10.0).
• The detailed content of the data files can found in a README file.

w2dynamics calculations

• DMFT calculations are done in three iterations, each involving different numbers of DMFT steps and statistics.
• Corresponding input files _Parameters_dmft_iter.in, _Parameters_dmft_iter_2.in, and _Parameters_dmft_stat.in can be found in the folder input_files/w2dynamics/, and are executed in that order.
• The output of the last iteration is contained in 1p-data.hdf5, including the self-energy on the Matsubara axis.

DGApy calculations

•  In addition to the single-particle data in 1p-data.hdf5, DGApy requires the two-particle DMFT data contained in g4iw_sym.hdf5.
• The corresponding input file _Parameters_vertex.in for w2dynamics can be found in input_files/w2dynamics/. Note that the DMFT output will contain the full Vertex.hdf5. To get g4iw_sym.hdf5 one needs to execute sym1b (part of DGApy) in the same folder where Vertex.hdf5 is located.
• The resulting self-energy on the Matsubara axis is contained in siwk_dga.npy files.

ana_cont

• Analytical continuation of the self-energy to the real-frequency axis was performed using MaxEnt as implemented in the ana_cont python package; model for fitting was flat and chi2kink method was used to determine the hyperparameter alpha.
• For temperatures T = 100/t and T = 15/t, number of fermionic Matsubara frequencies taken was 800 and 200, while the real-frequency grid was taken to be linear with 1001 points in the range [-50,50].
• Errors for DMFT self-energies can be found in 1p-data.hdf5, while for DGA results it is taken to be 1e-3; preblur was set to 1e-3 in all calculations.
• Analyically continued DMFT self-energy is located in self_energy.npz files, while analytically continued DGA self-energy in self_energy_nw1001_nk400_delta0.04.npy. Note that the interpolation in both momentum and frequency space may be employed to get better resolution. In addition, a constant imaginary part of 0.04 was added to the DGA self-energy to improve stability of results.