Tools for analysis

This section explains how to use some tools of the package in order to analyse the data.

There are two practical tools for which a self energy on the real axis is not needed, namely:

However, a real frequency self energy has to be provided by the user for the methods:

  • dos_parproj_basis for the momentum-integrated spectral function including self energy effects and
  • spaghettis for the momentum-resolved spectral function (i.e. ARPES)

Warning

This package does NOT provide an explicit method to do an analytic continuation of the self energies and Green functions from Matsubara frequencies to the real frequency axis! There are methods included e.g. in the ALPS package, which can be used for these purposes. Keep in mind that all these methods have to be used very carefully!

Initialisation

All tools described below are collected in an extension of the SumkDFT class and are loaded by importing the module SumkDFTTools:

from pytriqs.applications.dft.sumk_dft_tools import *

The initialisation of the class is equivalent to that of the SumkDFT class:

SK = SumkDFTTools(hdf_file = filename + '.h5')

Note that all routines available in SumkDFT are also available here.

If required, we have to load and initialise the real frequency self energy. Most conveniently, you have your self energy already stored as a real frequency BlockGf object in a hdf5 file:

ar = HDFArchive('case.h5', 'a')
SigmaReFreq = ar['dmft_output']['Sigma_w']

You may also have your self energy stored in text files. For this case the TRIQS library offers the function read_gf_from_txt(), which is able to load the data from text files of one Greens function block into a real frequency ReFreqGf object. Loading each block separately and building up a :class:´BlockGf <pytriqs.gf.local.BlockGf>´ is done with:

from pytriqs.gf.local.tools import *
# get block names
n_list = [n for n,nl in SK.gf_struct_solver[0].iteritems()]
# load sigma for each block - in this example sigma is composed of 1x1 blocks
g_blocks = [read_gf_from_txt(block_txtfiles=[['Sigma_'+name+'.dat']], block_name=n) for n in n_list]
# put the data into a BlockGf object
SigmaReFreq = BlockGf(name_list=n_list, block_list=g_blocks, make_copies=False)

where:

  • block_txtfiles is a rank 2 square np.array(str) or list[list[str]] holding the file names of one block and
  • block_name is the name of the block.

It is important that each data file has to contain three columns: the real frequency mesh, the real part and the imaginary part of the self energy - exactly in this order! The mesh should be the same for all files read in and non-uniform meshes are not supported.

Finally, we set the self energy into the SK object:

SK.set_Sigma([SigmaReFreq])

and additionally set the chemical potential and the double counting correction from the DMFT calculation:

chemical_potential, dc_imp, dc_energ = SK.load(['chemical_potential','dc_imp','dc_energ'])
SK.set_mu(chemical_potential)
SK.set_dc(dc_imp,dc_energ)
del ar

Density of states of the Wannier orbitals

For plotting the density of states of the Wannier orbitals, you type:

SK.dos_wannier_basis(broadening=0.03, mesh=[om_min, om_max, n_om], with_Sigma=False, with_dc=False, save_to_file=True)

which produces plots between the real frequencies om_min and om_max, using a mesh of n_om points. The parameter broadening defines an additional Lorentzian broadening, and has the default value of 0.01 eV. To check the Wannier density of states after the projection set with_Sigma and with_dc to False. If save_to_file is set to True the output is printed into the files

  • DOS_wannier_(sp).dat: The total DOS, where (sp) stands for up, down, or combined ud. The latter case is relevant for calculations including spin-orbit interaction.
  • DOS_wannier_(sp)_proj(i).dat: The DOS projected to an orbital with index (i). The index (i) refers to the indices given in SK.shells.
  • DOS_wannier_(sp)_proj(i)_(m)_(n).dat: As above, but printed as orbitally-resolved matrix in indices (m) and (n). For d orbitals, it gives the DOS separately for, e.g., \(d_{xy}\), \(d_{x^2-y^2}\), and so on,

otherwise, the output is returned by the function for a further usage in python.

Partial charges

Since we can calculate the partial charges directly from the Matsubara Green’s functions, we also do not need a real frequency self energy for this purpose. The calculation is done by:

SK.set_Sigma(SigmaImFreq)
dm = SK.partial_charges(beta=40.0, with_Sigma=True, with_dc=True)

which calculates the partial charges using the self energy, double counting, and chemical potential as set in the SK object. On return, dm is a list, where the list items correspond to the density matrices of all shells defined in the list SK.shells. This list is constructed by the Wien2k converter routines and stored automatically in the hdf5 archive. For the structure of dm, see also reference manual.

Correlated spectral function (with real frequency self energy)

To produce both the momentum-integrated (total density of states or DOS) and orbitally-resolved (partial/projected DOS) spectral functions we can execute:

SK.dos_parproj_basis(broadening=0.0, with_Sigma=True, with_dc=True, save_to_file=True)

The variable broadening is an additional Lorentzian broadening (default: 0.01 eV) applied to the resulting spectra. The output is written in the same way as described above for the Wannier density of states, but with filenames DOS_parproj_* instead.

Momentum resolved spectral function (with real frequency self energy)

Another quantity of interest is the momentum-resolved spectral function, which can directly be compared to ARPES experiments. First we have to execute lapw1, lapw2 -almd and dmftproj with the -band option and use the convert_bands_input routine, which converts the required files (for a more detailed description see Orbital construction and conversion). The spectral function is then calculated by typing:

SK.spaghettis(broadening=0.01,plot_shift=0.0,plot_range=None,ishell=None,save_to_file='Akw_')

Here, optional parameters are

  • shift: An additional shift added as (ik-1)*shift, where ik is the index of the k point. This is useful for plotting purposes. The default value is 0.0.
  • plotrange: A list with two entries, \(\omega_{min}\) and \(\omega_{max}\), which set the plot range for the output. The default value is None, in which case the full momentum range as given in the self energy is used.
  • ishell: An integer denoting the orbital index ishell onto which the spectral function is projected. The resulting function is saved in the files. The default value is None. Note for experts: The spectra are not rotated to the local coordinate system used in Wien2k.

The output is written as the 3-column files Akw(sp).dat, where (sp) is defined as above. The output format is k, \(\omega\), value.