mirror of
https://github.com/triqs/dft_tools
synced 2024-12-23 12:55:17 +01:00
6fc01806d0
I changed the expression for gf_struct so that it works with dft_tools 3. While I was at it, I took out the definition of 'l' since it's not used
282 lines
11 KiB
ReStructuredText
282 lines
11 KiB
ReStructuredText
.. _SrVO3:
|
|
|
|
On the example of SrVO3 we will discuss now how to set up a full working calculation,
|
|
including the initialization of the :ref:`CTHYB solver <triqscthyb:welcome>`.
|
|
Some additional parameter are introduced to make the calculation
|
|
more efficient. This is a more advanced example, which is
|
|
also suited for parallel execution.
|
|
|
|
For the convenience of the user, we provide also a full
|
|
python script (:download:`dft_dmft_cthyb.py <images_scripts/dft_dmft_cthyb.py>`).
|
|
The user has to adapt it to his own needs. How to execute your script is described :ref:`here<runpy>`.
|
|
|
|
The conversion will now be discussed in detail for the Wien2k and VASP packages.
|
|
For more details we refer to the :ref:`documentation <conversion>`.
|
|
|
|
|
|
DFT (Wien2k) and Wannier orbitals
|
|
=================================
|
|
|
|
DFT setup
|
|
---------
|
|
|
|
First, we do a DFT calculation, using the Wien2k package. As main input file we have to provide the so-called struct file :file:`SrVO3.struct`. We use the following:
|
|
|
|
.. literalinclude:: images_scripts/SrVO3.struct
|
|
|
|
Instead of going through the whole initialisation process, we can use ::
|
|
|
|
init -b -vxc 5 -numk 5000
|
|
|
|
This is setting up a non-magnetic calculation, using the LDA and 5000 k-points in the full Brillouin zone. As usual, we start the DFT self consistent cycle by the Wien2k script ::
|
|
|
|
run
|
|
|
|
Wannier orbitals
|
|
----------------
|
|
|
|
As a next step, we calculate localised orbitals for the t2g orbitals with :program:`dmftproj`.
|
|
We create the following input file, :file:`SrVO3.indmftpr`
|
|
|
|
.. literalinclude:: images_scripts/SrVO3.indmftpr
|
|
|
|
Details on this input file and how to use :program:`dmftproj` are described :ref:`here <convWien2k>`.
|
|
|
|
To prepare the input data for :program:`dmftproj` we first execute lapw2 with the `-almd` option ::
|
|
|
|
x lapw2 -almd
|
|
|
|
Then :program:`dmftproj` is executed in its default mode (i.e. without spin-polarization or spin-orbit included) ::
|
|
|
|
dmftproj
|
|
|
|
This program produces the necessary files for the conversion to the hdf5 file structure. This is done using
|
|
the python module :class:`Wien2kConverter <dft.converters.wien2k.Wien2kConverter>`.
|
|
A simple python script that initialises the converter is::
|
|
|
|
from triqs_dft_tools.converters.wien2k import *
|
|
Converter = Wien2kConverter(filename = "SrVO3")
|
|
|
|
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 everything that is necessary for the DMFT calculation in the file :file:`SrVO3.h5`.
|
|
|
|
|
|
The DMFT calculation
|
|
====================
|
|
|
|
The DMFT script itself is, except very few details, independent of the DFT package that was used to calculate the local orbitals.
|
|
As soon as one has converted everything to the hdf5 format, the following procedure is practially the same.
|
|
|
|
Loading modules
|
|
---------------
|
|
|
|
First, we load the necessary modules::
|
|
|
|
from triqs_dft_tools.sumk_dft import *
|
|
from triqs.gf import *
|
|
from h5 import HDFArchive
|
|
from triqs.operators.util import *
|
|
from triqs_cthyb import *
|
|
import triqs.utility.mpi as mpi
|
|
|
|
The last two lines load the modules for the construction of the
|
|
:ref:`CTHYB solver <triqscthyb:welcome>`.
|
|
|
|
Initializing SumkDFT
|
|
--------------------
|
|
|
|
We define some parameters, which should be self-explanatory::
|
|
|
|
dft_filename = 'SrVO3' # filename
|
|
U = 4.0 # interaction parameters
|
|
J = 0.65
|
|
beta = 40 # inverse temperature
|
|
loops = 15 # number of DMFT loops
|
|
mix = 0.8 # mixing factor of Sigma after solution of the AIM
|
|
dc_type = 1 # DC type: 0 FLL, 1 Held, 2 AMF
|
|
use_blocks = True # use bloc structure from DFT input
|
|
prec_mu = 0.0001 # precision of chemical potential
|
|
|
|
|
|
And next, we can initialize the :class:`SumkDFT <dft.sumk_dft.SumkDFT>` class::
|
|
|
|
SK = SumkDFT(hdf_file=dft_filename+'.h5',use_dft_blocks=use_blocks)
|
|
|
|
Initializing the solver
|
|
-----------------------
|
|
|
|
We also have to specify the :ref:`CTHYB solver <triqscthyb:welcome>` related settings.
|
|
We assume that the DMFT script for SrVO3 is executed on 16 cores. A sufficient set
|
|
of parameters for a first guess is::
|
|
|
|
p = {}
|
|
# solver
|
|
p["random_seed"] = 123 * mpi.rank + 567
|
|
p["length_cycle"] = 200
|
|
p["n_warmup_cycles"] = 100000
|
|
p["n_cycles"] = 1000000
|
|
# tail fit
|
|
p["perform_tail_fit"] = True
|
|
p["fit_max_moment"] = 4
|
|
p["fit_min_n"] = 30
|
|
p["fit_max_n"] = 60
|
|
|
|
Here we use a tail fit to deal with numerical noise of higher Matsubara frequencies.
|
|
For other options and more details on the solver parameters, we refer the user to
|
|
the :ref:`CTHYB solver <triqscthyb:welcome>` documentation.
|
|
It is important to note that the solver parameters have to be adjusted for
|
|
each material individually. A guide on how to set the tail fit parameters is given
|
|
:ref:`below <tailfit>`.
|
|
|
|
|
|
The next step is to initialize the
|
|
:class:`solver class <triqs_cthyb.Solver>`.
|
|
It consist of two parts:
|
|
|
|
#. Calculating the multi-band interaction matrix, and constructing the
|
|
interaction Hamiltonian.
|
|
#. Initializing the solver class itself.
|
|
|
|
The first step is done using methods of the :ref:`TRIQS <triqslibs:welcome>` library::
|
|
|
|
n_orb = SK.corr_shells[0]['dim']
|
|
spin_names = ["up","down"]
|
|
orb_names = [i for i in range(n_orb)]
|
|
# Use GF structure determined by DFT blocks:
|
|
gf_struct = SK.gf_struct_solver_list[0]
|
|
# Construct U matrix for density-density calculations:
|
|
Umat, Upmat = U_matrix_kanamori(n_orb=n_orb, U_int=U, J_hund=J)
|
|
|
|
We assumed here that we want to use an interaction matrix with
|
|
Kanamori definitions of :math:`U` and :math:`J`.
|
|
|
|
Next, we construct the Hamiltonian and the solver::
|
|
|
|
h_int = h_int_density(spin_names, orb_names, map_operator_structure=SK.sumk_to_solver[0], U=Umat, Uprime=Upmat)
|
|
S = Solver(beta=beta, gf_struct=gf_struct)
|
|
|
|
As you see, we take only density-density interactions into
|
|
account. Other Hamiltonians with, e.g. with full rotational invariant interactions are:
|
|
|
|
* h_int_kanamori
|
|
* h_int_slater
|
|
|
|
For other choices of the interaction matrices (e.g Slater representation) or
|
|
Hamiltonians, we refer to the reference manual of the :ref:`TRIQS <triqslibs:welcome>`
|
|
library.
|
|
|
|
As a last step, we initialize the subgroup in the hdf5 archive to store the results::
|
|
|
|
if mpi.is_master_node():
|
|
with HDFArchive(dft_filename+'.h5') as ar:
|
|
if (not ar.is_group('dmft_output')):
|
|
ar.create_group('dmft_output')
|
|
|
|
DMFT cycle
|
|
----------
|
|
|
|
Now we can go to the definition of the self-consistency step. It consists again
|
|
of the basic steps discussed in the :ref:`previous section <singleshot>`, with
|
|
some additional refinements::
|
|
|
|
for iteration_number in range(1,loops+1):
|
|
if mpi.is_master_node(): print("Iteration = ", iteration_number)
|
|
|
|
SK.symm_deg_gf(S.Sigma_iw,ish=0) # symmetrizing Sigma
|
|
SK.set_Sigma([ S.Sigma_iw ]) # put Sigma into the SumK class
|
|
chemical_potential = SK.calc_mu( precision = prec_mu ) # find the chemical potential for given density
|
|
S.G_iw << SK.extract_G_loc()[0] # calc the local Green function
|
|
mpi.report("Total charge of Gloc : %.6f"%S.G_iw.total_density())
|
|
|
|
# In the first loop, init the DC term and the real part of Sigma:
|
|
if (iteration_number==1):
|
|
dm = S.G_iw.density()
|
|
SK.calc_dc(dm, U_interact = U, J_hund = J, orb = 0, use_dc_formula = dc_type)
|
|
S.Sigma_iw << SK.dc_imp[0]['up'][0,0]
|
|
|
|
# Calculate new G0_iw to input into the solver:
|
|
S.G0_iw << S.Sigma_iw + inverse(S.G_iw)
|
|
S.G0_iw << inverse(S.G0_iw)
|
|
|
|
# Solve the impurity problem:
|
|
S.solve(h_int=h_int, **p)
|
|
|
|
# Solved. Now do post-solution stuff:
|
|
mpi.report("Total charge of impurity problem : %.6f"%S.G_iw.total_density())
|
|
|
|
# Now mix Sigma and G with factor mix, if wanted:
|
|
if (iteration_number>1):
|
|
if mpi.is_master_node():
|
|
with HDFArchive(dft_filename+'.h5','r') as ar:
|
|
mpi.report("Mixing Sigma and G with factor %s"%mix)
|
|
S.Sigma_iw << mix * S.Sigma_iw + (1.0-mix) * ar['dmft_output']['Sigma_iw']
|
|
S.G_iw << mix * S.G_iw + (1.0-mix) * ar['dmft_output']['G_iw']
|
|
S.G_iw << mpi.bcast(S.G_iw)
|
|
S.Sigma_iw << mpi.bcast(S.Sigma_iw)
|
|
|
|
# Write the final Sigma and G to the hdf5 archive:
|
|
if mpi.is_master_node():
|
|
with HDFArchive(dft_filename+'.h5') as ar:
|
|
ar['dmft_output']['iterations'] = iteration_number
|
|
ar['dmft_output']['G_0'] = S.G0_iw
|
|
ar['dmft_output']['G_tau'] = S.G_tau
|
|
ar['dmft_output']['G_iw'] = S.G_iw
|
|
ar['dmft_output']['Sigma_iw'] = S.Sigma_iw
|
|
|
|
# Set the new double counting:
|
|
dm = S.G_iw.density() # compute the density matrix of the impurity problem
|
|
SK.calc_dc(dm, U_interact = U, J_hund = J, orb = 0, use_dc_formula = dc_type)
|
|
|
|
# Save stuff into the user_data group of hdf5 archive in case of rerun:
|
|
SK.save(['chemical_potential','dc_imp','dc_energ'])
|
|
|
|
|
|
This is all we need for the DFT+DMFT calculation.
|
|
You can see in this code snippet, that all results of this calculation
|
|
will be stored in a separate subgroup in the hdf5 file, called `dmft_output`.
|
|
Note that this script performs 15 DMFT cycles, but does not check for
|
|
convergence. Of course, it would be possible to build in convergence criteria.
|
|
A simple check for convergence can be also done if you store multiple quantities
|
|
of each iteration and analyse the convergence by hand. In general, it is advisable
|
|
to start with a lower statistics (less measurements), but then increase it at a
|
|
point close to converged results (e.g. after a few initial iterations). This helps
|
|
to keep computational costs low during the first iterations.
|
|
|
|
Using the Kanamori Hamiltonian and the parameters above (but on 16 cores),
|
|
your self energy after the **first iteration** should look like the
|
|
self energy shown below.
|
|
|
|
.. image:: images_scripts/SrVO3_Sigma_iw_it1.png
|
|
:width: 700
|
|
:align: center
|
|
|
|
.. _tailfit:
|
|
|
|
Tail fit parameters
|
|
-------------------
|
|
|
|
A good way to identify suitable tail fit parameters is by "human inspection".
|
|
Therefore disabled the tail fitting first::
|
|
|
|
p["perform_tail_fit"] = False
|
|
|
|
and perform only one DMFT iteration. The resulting self energy can be tail fitted by hand::
|
|
|
|
Sigma_iw_fit = S.Sigma_iw.copy()
|
|
Sigma_iw_fit << tail_fit(S.Sigma_iw, fit_max_moment = 4, fit_min_n = 40, fit_max_n = 160)[0]
|
|
|
|
Plot the self energy and adjust the tail fit parameters such that you obtain a
|
|
proper fit. The :meth:`fit_tail function <triqs.gf.tools.tail_fit>` is part
|
|
of the :ref:`TRIQS <triqslibs:welcome>` library.
|
|
|
|
For a self energy which is going to zero for :math:`i\omega \rightarrow 0` our suggestion is
|
|
to start the tail fit (:emphasis:`fit_min_n`) at a Matsubara frequency considerable above the minimum
|
|
of the self energy and to stop (:emphasis:`fit_max_n`) before the noise fully takes over.
|
|
If it is difficult to find a reasonable fit in this region you should increase
|
|
your statistics (number of measurements). Keep in mind that :emphasis:`fit_min_n`
|
|
and :emphasis:`fit_max_n` also depend on :math:`\beta`.
|