mirror of https://github.com/triqs/dft_tools
147 lines
7.9 KiB
ReStructuredText
147 lines
7.9 KiB
ReStructuredText
.. _analysis:
|
||
|
||
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:
|
||
|
||
* :meth:`dos_wannier_basis <dft.sumk_dft_tools.SumkDFTTools.dos_wannier_basis>` for the density of states of the Wannier orbitals and
|
||
* :meth:`partial_charges <dft.sumk_dft_tools.SumkDFTTools.partial_charges>` for the partial charges according to the Wien2k definition.
|
||
|
||
However, a real-frequency self energy has to be provided by the user for the methods:
|
||
|
||
* :meth:`dos_parproj_basis <dft.sumk_dft_tools.SumkDFTTools.dos_parproj_basis>` for the momentum-integrated spectral function including self energy effects and
|
||
* :meth:`spaghettis <dft.sumk_dft_tools.SumkDFTTools.spaghettis>` for the momentum-resolved spectral function (i.e. ARPES)
|
||
|
||
.. note::
|
||
This package does NOT provide an explicit method to do an **analytic continuation** of
|
||
self energies and Green functions from Matsubara frequencies to the real-frequency axis,
|
||
but a list of options available within the TRIQS framework is given :ref:`here <ac>`.
|
||
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 :class:`SumkDFT <dft.sumk_dft.SumkDFT>` class and are
|
||
loaded by importing the module :class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>`::
|
||
|
||
from triqs_dft_tools.sumk_dft_tools import *
|
||
|
||
The initialisation of the class is equivalent to that of the :class:`SumkDFT <dft.sumk_dft.SumkDFT>`
|
||
class::
|
||
|
||
SK = SumkDFTTools(hdf_file = filename + '.h5')
|
||
|
||
Note that all routines available in :class:`SumkDFT <dft.sumk_dft.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 :class:`BlockGf <pytriqs.gf.BlockGf>` object
|
||
in a hdf5 file::
|
||
|
||
with HDFArchive('case.h5', 'r') as ar:
|
||
SigmaReFreq = ar['dmft_output']['Sigma_w']
|
||
|
||
You may also have your self energy stored in text files. For this case the :ref:`TRIQS <triqslibs:welcome>` library offers
|
||
the function :meth:`read_gf_from_txt`, which is able to load the data from text files of one Green function block
|
||
into a real-frequency :class:`ReFreqGf <pytriqs.gf.ReFreqGf>` object. Loading each block separately and
|
||
building up a :class:´BlockGf <pytriqs.gf.BlockGf>´ is done with::
|
||
|
||
from pytriqs.gf.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)
|
||
|
||
.. _dos_wannier:
|
||
|
||
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., :math:`d_{xy}`, :math:`d_{x^2-y^2}`, and so on,
|
||
|
||
otherwise, the output is returned by the function for a further usage in :program:`python`.
|
||
|
||
Partial charges
|
||
---------------
|
||
|
||
Since we can calculate the partial charges directly from the Matsubara Green 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 :meth:`reference manual <dft.sumk_dft_tools.SumkDFTTools.partial_charges>`.
|
||
|
||
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 :ref:`Wannier density of states <dos_wannier>`, 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 :program:`dmftproj` with the `-band`
|
||
option and use the :meth:`convert_bands_input <dft.converters.wien2k_converter.Wien2kConverter.convert_bands_input>`
|
||
routine, which converts the required files (for a more detailed description see :ref:`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, :math:`\omega_{min}` and :math:`\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`, :math:`\omega`, `value`.
|