dft_tools/doc/guide/conversion.rst

.. _conversion:

Orbital construction and conversion
===================================

The first step for a DMFT calculation is to provide the necessary
input based on a DFT calculation. We will not review how to do the DFT
calculation here in this documentation, but refer the user to the
documentation and tutorials that come with the actual DFT
package. Here, we will describe how to use output created by Wien2k,
as well as how to use the light-weight general interface.

Interface with Wien2k
---------------------

We assume that the user has obtained a self-consistent solution of the
Kohn-Sham equations. We further have to require that the user is
familiar with the main in/output files of Wien2k, and how to run
the DFT code.

Conversion for the DMFT self-consistency cycle
""""""""""""""""""""""""""""""""""""""""""""""

First, we have to write the necessary
quantities into a file that can be processed further by invoking in a
shell the command 
  
  `x lapw2 -almd`

We note that any other flag for lapw2, such as -c or -so (for
spin-orbit coupling) has to be added also to this line. This creates
some files that we need for the Wannier orbital construction.

The orbital construction itself is done by the Fortran program
:program:`dmftproj`. For an extensive manual to this program see
:download:`TutorialDmftproj.pdf <images_scripts/TutorialDmftproj.pdf>`.
Here we will only describe the basic steps.

Let us take the compound SrVO3, a commonly used
example for DFT+DMFT calculations. The input file for
:program:`dmftproj` looks like 

.. literalinclude:: images_scripts/SrVO3.indmftpr

The first three lines give the number of inequivalent sites, their
multiplicity (to be in accordance with the Wien2k *struct* file) and
the maximum orbital quantum number :math:`l_{max}`. In our case our
struct file contains the atoms in the order Sr, V, O.

Next we have to
specify for each of the inequivalent sites, whether we want to treat
their orbitals as correlated or not. This information is given by the
following 3 to 5 lines:

#. We specify which basis set is used (complex or cubic
   harmonics).
#. The four numbers refer to *s*, *p*, *d*, and *f* electrons,
   resp. Putting 0 means doing nothing, putting 1 will calculate
   **unnormalized** projectors in compliance with the Wien2k
   definition. The important flag is 2, this means to include these
   electrons as correlated electrons, and calculate normalized Wannier
   functions for them. In the example above, you see that only for the
   vanadium *d* we set the flag to 2. If you want to do simply a DMFT
   calculation, then set everything to 0, except one flag 2 for the
   correlated electrons.
#. In case you have a irrep splitting of the correlated shell, you can
   specify here how many irreps you have. You see that we put 2, since
   eg and t2g symmetries are irreps in this cubic case. If you don't
   want to use this splitting, just put 0.
#. (optional) If you specifies a number different from 0 in above line, you have
   to tell now, which of the irreps you want to be treated
   correlated. We want to t2g, and not the eg, so we set 0 for eg and
   1 for t2g. Note that the example above is what you need in 99% of
   the cases when you want to treat only t2g electrons. For eg's only
   (e.g. nickelates), you set 10 and 01 in this line.
#. (optional) If you have specified a correlated shell for this atom,
   you have to tell if spin-orbit coupling should be taken into
   account. 0 means no, 1 is yes.

These lines have to be repeated for each inequivalent atom.

The last line gives the energy window, relative to the Fermi energy,
that is used for the projective Wannier functions. Note that, in
accordance with Wien2k, we give energies in Rydberg units!

After setting up this input file, you run:

  `dmftproj`

Again, adding possible flags like -so for spin-orbit coupling. This
program produces the following files (in the following, take *case* as
the standard Wien2k place holder, to be replaced by the actual working
directory name):  

 * :file:`case.ctqmcout` and :file:`case.symqmc` containing projector
   operators and symmetry operations for orthonormalized Wannier
   orbitals, respectively. 
 * :file:`case.parproj` and :file:`case.sympar` containing projector
   operators and symmetry operations for uncorrelated states,
   respectively. These files are needed for projected
   density-of-states or spectral-function calculations in
   post-processing only. 
 * :file:`case.oubwin` needed for the charge density recalculation in
   the case of fully self-consistent DFT+DMFT run (see below). 

Now we convert these files into an hdf5 file that can be used for the
DMFT calculations. For this purpose we
use the python module :class:`Wien2kConverter <dft.converters.wien2k_converter.Wien2kConverter>`. It is initialized as::

  from pytriqs.applications.dft.converters.wien2k_converter import *
  Converter = Wien2kConverter(filename = case)

The only necessary parameter to this construction is the parameter `filename`.
It has to be the root of the files produces by dmftproj. For our
example, the :program:`Wien2k` naming convention is that all files are
called the same, for instance
:file:`SrVO3.*`, so you would give `filename = "SrVO3"`. The constructor opens
an hdf5 archive, named :file:`case.h5`, where all the data is
stored. For other parameters of the constructor please visit the
:ref:`refconverters` section of the reference manual.

After initializing the interface module, we can now convert the input
text files to the hdf5 archive by::

  Converter.convert_dft_input()

This reads all the data, and stores it in the file :file:`case.h5`. 
In this step, the files :file:`case.ctqmcout` and
:file:`case.symqmc` 
have to be present in the working directory.

After this step, all the necessary information for the DMFT loop is
stored in the hdf5 archive, where the string variable
`Converter.hdf_filename` gives the file name of the archive.

At this point you should use the method :meth:`dos_wannier_basis <dft.sumk_dft_tools.SumkDFTTools.dos_wannier_basis>`
contained in the module :class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>` to check the density of
states of the Wannier orbitals (see :ref:`analysis`).

You have now everything for performing a DMFT calculation, and you can
proceed with the section on :ref:`single-shot DFT+DMFT calculations <singleshot>`.

Data for post-processing
""""""""""""""""""""""""

In case you want to do post-processing of your data using the module
:class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>`, some more files
have to be converted to the hdf5 archive. For instance, for
calculating the partial density of states or partial charges
consistent with the definition of :program:`Wien2k`, you have to invoke::

  Converter.convert_parproj_input()

This reads and converts the files :file:`case.parproj` and
:file:`case.sympar`.

If you want to plot band structures, one has to do the
following. First, one has to do the Wien2k calculation on the given
:math:`\mathbf{k}`-path, and run :program:`dmftproj` on that path:
	
  |  `x lapw1 -band`
  |  `x lapw2 -band -almd`
  |  `dmftproj -band`


Again, maybe with the optional additional extra flags according to
Wien2k. Now we use a routine of the converter module allows to read
and convert the input for :class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>`::

  Converter.convert_bands_input()
       
After having converted this input, you can further proceed with the
:ref:`analysis`. For more options on the converter module, please have
a look at the :ref:`refconverters` section of the reference manual.

Data for transport calculations
"""""""""""""""""""""""""""""""

For the transport calculations, the situation is a bit more involved,
since we need also the :program:`optics` package of Wien2k. Please
look at the section on :ref:`Transport` to see how to do the necessary
steps, including the conversion.
  
  
A general H(k)
--------------

In addition to the more complicated Wien2k converter,
:program:`DFTTools` contains also a light converter. It takes only
one inputfile, and creates the necessary hdf outputfile for
the DMFT calculation. The header of this input file has to have the
following format:

.. literalinclude:: images_scripts/case.hk

The lines of this header define
		    
#. Number of :math:`\mathbf{k}`-points used in the calculation
#. Electron density for setting the chemical potential
#. Number of correlated atoms in the unit cell
#. The next line contains four numbers: index of the atom, index
   of the correlated shell, :math:`l` quantum number, dimension
   of this shell. Repeat this line for each correlated atom.
#. The last line contains several numbers: the number of irreducible
   representations, and then the dimensions of the irreps. One
   possibility is as the example above, another one would be 2
   2 3. This would mean, 2 irreps (eg and t2g), of dimension 2 and 3,
   resp.

After these header lines, the file has to contain the Hamiltonian
matrix in orbital space. The standard convention is that you give for
each :math:`\mathbf{k}`-point first the matrix of the real part, then the
matrix of the imaginary part, and then move on to the next :math:`\mathbf{k}`-point.

The converter itself is used as::

  from pytriqs.applications.dft.converters.hk_converter import *
  Converter = HkConverter(filename = hkinputfile)
  Converter.convert_dft_input()
  
where :file:`hkinputfile` is the name of the input file described
above. This produces the hdf file that you need for a DMFT calculation.

For more options of this converter, have a look at the
:ref:`refconverters` section of the reference manual.


Wannier90 Converter
-------------------

Using this converter it is possible to convert the output of
`wannier90 <http://wannier.org>`_
Maximally Localized Wannier Functions (MLWF) and create a HDF5 archive
suitable for one-shot DMFT calculations with the
:class:`SumkDFT <dft.sumk_dft.SumkDFT>` class.

The user must supply two files in order to run the Wannier90 Converter:

#. The file :file:`seedname_hr.dat`, which contains the DFT Hamiltonian
   in the MLWF basis calculated through :program:`wannier90` with ``hr_plot = true``
   (please refer to the :program:`wannier90` documentation).
#. A file named :file:`seedname.inp`, which contains the required
   information about the :math:`\mathbf{k}`-point mesh, the electron density,
   the correlated shell structure, ... (see below).

Here and in the following, the keyword ``seedname`` should always be intended
as a placeholder for the actual prefix chosen by the user when creating the
input for :program:`wannier90`.
Once these two files are available, one can use the converter as follows::

    from pytriqs.applications.dft.converters import Wannier90Converter
    Converter = Wannier90Converter(seedname='seedname')
    Converter.convert_dft_input()

The converter input :file:`seedname.inp` is a simple text file with
the following format:

.. literalinclude:: images_scripts/LaVO3_w90.inp

The example shows the input for the perovskite crystal of LaVO\ :sub:`3`
in the room-temperature `Pnma` symmetry. The unit cell contains four
symmetry-equivalent correlated sites (the V atoms) and the total number
of electrons per unit cell is 8 (see second line).
The first line specifies how to generate the :math:`\mathbf{k}`-point
mesh that will be used to obtain :math:`H(\mathbf{k})`
by Fourier transforming :math:`H(\mathbf{R})`.
Currently implemented options are:

* :math:`\Gamma`-centered uniform grid with dimensions
  :math:`n_{k_x} \times n_{k_y} \times n_{k_z}`;
  specify ``0`` followed by the three grid dimensions,
  like in the example above
* :math:`\Gamma`-centered uniform grid with dimensions 
  automatically determined by the converter (from the number of
  :math:`\mathbf{R}` vectors found in :file:`seedname_hr.dat`);
  just specify ``-1``

Inside :file:`seedname.inp`, it is crucial to correctly specify the
correlated shell structure, which depends on the contents of the
:program:`wannier90` output :file:`seedname_hr.dat` and on the order
of the MLWFs contained in it.

The number of MLWFs must be equal to, or greater than the total number
of correlated orbitals (i.e., the sum of all ``dim`` in :file:`seedname.inp`).
If the converter finds fewer MLWFs inside :file:`seedname_hr.dat`, then it
stops with an error; if it finds more MLWFs, then it assumes that the
additional MLWFs correspond to uncorrelated orbitals (e.g., the O-\ `2p` shells).
When reading the hoppings :math:`\langle w_i | H(\mathbf{R}) | w_j \rangle`
(where :math:`w_i` is the :math:`i`-th MLWF), the converter also assumes that
the first indices correspond to the correlated shells (in our example,
the V-t\ :sub:`2g` shells). Therefore, the MLWFs corresponding to the
uncorrelated shells (if present) must be listed **after** those of the 
correlated shells.
With the :program:`wannier90` code, this can be achieved this by listing the
projections for the uncorrelated shells after those for the correlated shells.
In our `Pnma`-LaVO\ :sub:`3` example, for instance, we could use::

    Begin Projections
     V:l=2,mr=2,3,5:z=0,0,1:x=-1,1,0
     O:l=1:mr=1,2,3:z=0,0,1:x=-1,1,0
    End Projections

where the ``x=-1,1,0`` option indicates that the V--O bonds in the octahedra are
rotated by (approximatively) 45 degrees with respect to the axes of the `Pbnm` cell.

The converter will analyze the matrix elements of the local Hamiltonian
to find the symmetry matrices `rot_mat` needed for the global-to-local
transformation of the basis set for correlated orbitals
(see section :ref:`hdfstructure`).
The matrices are obtained by finding the unitary transformations that diagonalize
:math:`\langle w_i | H_I(\mathbf{R}=0,0,0) | w_j \rangle`, where :math:`I` runs
over the correlated shells and `i,j` belong to the same shell (more details elsewhere...).
If two correlated shells are defined as equivalent in :file:`seedname.inp`,
then the corresponding eigenvalues have to match within a threshold of 10\ :sup:`-5`,
otherwise the converter will produce an error/warning.
If this happens, please carefully check your data in :file:`seedname_hr.dat`.
This method might fail in non-trivial cases (i.e., more than one correlated
shell is present) when there are some degenerate eigenvalues:
so far tests have not shown any issue, but one must be careful in those cases
(the converter will print a warning message).

The current implementation of the Wannier90 Converter has some limitations:

* Since :program:`wannier90` does not make use of symmetries (symmetry-reduction
  of the :math:`\mathbf{k}`-point grid is not possible), the converter always
  sets ``symm_op=0`` (see the :ref:`hdfstructure` section).
* No charge self-consistency possible at the moment.
* Calculations with spin-orbit (``SO=1``) are not supported.
* The spin-polarized case (``SP=1``) is not yet tested.
* The post-processing routines in the module
  :class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>`
  were not tested with this converter.
* ``proj_mat_all`` are not used, so there are no projectors onto the
  uncorrelated orbitals for now.

     
MPI issues
----------

The interface packages are written such that all the file operations
are done only on the master node. In general, the philosophy of the
package is that whenever you read in something from the archive
yourself, you have to *manually* broadcast it to the nodes. An
exception to this rule is when you use routines from :class:`SumkDFT <dft.sumk_dft.SumkDFT>`
or :class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>`, where the broadcasting is done for you.

Interfaces to other packages
----------------------------

Because of the modular structure, it is straight forward to extend the :ref:`TRIQS <triqslibs:welcome>` package
in order to work with other band-structure codes. The only necessary requirement is that
the interface module produces an hdf5 archive, that stores all the data in the specified
form. For the details of what data is stored in detail, see the
:ref:`hdfstructure` part of the reference manual.