mirror of
https://github.com/triqs/dft_tools
synced 2024-12-22 12:23:41 +01:00
166 lines
7.3 KiB
ReStructuredText
166 lines
7.3 KiB
ReStructuredText
.. highlight:: python
|
|
|
|
.. _singleshot:
|
|
|
|
Single-shot DFT+DMFT
|
|
====================
|
|
|
|
After having set up the hdf5 archive, we can now proceed to our first DFT+DMFT calculation.
|
|
It consists of initialization steps, and the actual DMFT self-consistency loop,
|
|
With the code snippets below you can build your own script and target
|
|
it to your needs. Little examples on :ref:`mixing <mixing>` and on
|
|
:ref:`restarting from a previous calculation <restartcalc>` at the end of this page
|
|
should also demonstrate how simple you can modify your own DMFT script. A full working
|
|
calculation for SrVO3 is discussed in the :ref:`next section <SrVO3>`.
|
|
|
|
|
|
Initialization of the calculation
|
|
---------------------------------
|
|
|
|
Before doing the actual calculation, we have to initialize all needed objects.
|
|
The first thing is the :class:`SumkDFT <dft.sumk_dft.SumkDFT>` class.
|
|
It contains all basic routines that are necessary to perform a summation in k-space
|
|
to get the local quantities used in DMFT. It is initialized by::
|
|
|
|
from triqs_dft_tools.sumk_dft import *
|
|
SK = SumkDFT(hdf_file = filename + '.h5')
|
|
|
|
|
|
Setting up the impurity solver
|
|
------------------------------
|
|
|
|
The next step is to setup an impurity solver. There are different
|
|
solvers available within the :ref:`TRIQS <triqslibs:welcome>` framework.
|
|
E.g. for :ref:`SrVO3 <SrVO3>`, we will use the hybridization
|
|
expansion :ref:`CTHYB solver <triqscthyb:welcome>`. Later on, we will
|
|
see also the example of the `Hubbard-I solver <https://triqs.github.io/triqs/1.4/applications/hubbardI/>`_.
|
|
They all have in common, that they are called by an uniform command::
|
|
|
|
S.solve(params)
|
|
|
|
where :emphasis:`params` are the solver parameters and depend on the actual
|
|
solver. Setting up the :ref:`CTHYB solver <triqscthyb:welcome>` for SrVO3 is
|
|
discussed on the :ref:`next page <SrVO3>`. Here, let us now perform the DMFT
|
|
loop using the methods of :program:`DFTTools`, assuming that we have already
|
|
set up a working solver instance.
|
|
|
|
|
|
Doing the DMFT loop
|
|
-------------------
|
|
|
|
Having initialized the :class:`Sumk class <dft.sumk_dft.SumkDFT>`
|
|
and the solver, we can proceed with the actual DMFT part of the calculation.
|
|
We set up the loop over DMFT iterations and the self-consistency condition::
|
|
|
|
n_loops = 15
|
|
for iteration_number in range(n_loops) : # start the DMFT loop
|
|
SK.set_Sigma([ S.Sigma ]) # Put self energy to the SumK class
|
|
chemical_potential = SK.calc_mu() # calculate the chemical potential for the given density
|
|
S.G_iw << SK.extract_G_loc()[0] # extract the local Green function
|
|
S.G0_iw << inverse(S.Sigma_iw + inverse(S.G_iw)) # finally get G0, the input for the solver
|
|
|
|
S.solve(h_int=h_int, **p) # now solve the impurity problem
|
|
|
|
dm = S.G_iw.density() # Density matrix of the impurity problem
|
|
SK.calc_dc(dm, U_interact=U, J_hund=J, orb=0, use_dc_formula=1) # Set the double counting term
|
|
SK.save(['chemical_potential','dc_imp','dc_energ']) # Save data in the hdf5 archive
|
|
|
|
These steps are enough for a basic DMFT Loop.
|
|
After the self-consistency steps, which lead to a new :math:`G^0(i\omega)`,
|
|
the impurity solver is called. Different to model calculations, we have to do a few
|
|
more steps after this, because of the double-counting correction. We first
|
|
calculate the density of the impurity problem. Then, the routine :meth:`calc_dc <dft.sumk_dft.SumkDFT.calc_dc>`
|
|
takes as parameters this density matrix, the Coulomb interaction, Hund's rule
|
|
coupling, and the type of double-counting that should be used. Possible values
|
|
for :emphasis:`use_dc_formula` are:
|
|
|
|
* `0`: Full-localised limit (FLL)
|
|
* `1`: DC formula as given in K. Held, Adv. Phys. 56, 829 (2007).
|
|
* `2`: Around-mean-field (AMF)
|
|
|
|
At the end of the calculation, we can save the Green function and self energy into a file::
|
|
|
|
from pytriqs.archive import HDFArchive
|
|
import pytriqs.utility.mpi as mpi
|
|
if mpi.is_master_node():
|
|
ar = HDFArchive("YourDFTDMFTcalculation.h5",'w')
|
|
ar["G"] = S.G_iw
|
|
ar["Sigma"] = S.Sigma_iw
|
|
|
|
These are the essential steps necessary for a one-shot DFT+DMFT calculation.
|
|
For a detailed description of the :class:`SumkDFT <dft.sumk_dft.SumkDFT>`
|
|
routines, see the :ref:`reference manual <reference>`. To perform full charge self-consistent calculations, there
|
|
are some more things to consider, which we will see :ref:`later on <full_charge_selfcons>`.
|
|
|
|
.. _restartcalc:
|
|
|
|
|
|
Restarting a calculation
|
|
------------------------
|
|
|
|
Often only a few DMFT iterations are performed first, and thus, it is desirable to
|
|
carry out further iterations, e.g. to improve on the convergence. With a little modification
|
|
at the initialization stage (before the DMFT loop) it is possible to detect if previous runs
|
|
are present, or if the calculation should start from scratch::
|
|
|
|
previous_runs = 0
|
|
previous_present = False
|
|
if mpi.is_master_node():
|
|
with HDFArchive(dft_filename+'.h5','a') as f:
|
|
if 'dmft_output' in f:
|
|
ar = f['dmft_output']
|
|
if 'iterations' in ar:
|
|
previous_present = True
|
|
previous_runs = ar['iterations']
|
|
else:
|
|
f.create_group('dmft_output')
|
|
|
|
previous_runs = mpi.bcast(previous_runs)
|
|
previous_present = mpi.bcast(previous_present)
|
|
|
|
|
|
You can see from this code snippet, that removing the subgroup :emphasis:`dmft_results` from the
|
|
hdf file has the effect of reseting the calculation to the starting point. If there are previous
|
|
runs stored in the hdf5 archive, we can now load the self energy, the chemical potential and
|
|
double counting values of the last iteration::
|
|
|
|
if previous_present:
|
|
if mpi.is_master_node():
|
|
with HDFArchive(dft_filename+'.h5','r') as ar:
|
|
S.Sigma_iw << ar['dmft_output']['Sigma_iw']
|
|
|
|
S.Sigma_iw << mpi.bcast(S.Sigma_iw)
|
|
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)
|
|
|
|
The data is loaded only on the master node, and therefore we broadcast it to the slave nodes.
|
|
Be careful when storing the :emphasis:`iteration_number` as we also have to add the previous
|
|
iteration count::
|
|
|
|
ar['dmft_output']['iterations'] = iteration_number + previous_runs
|
|
|
|
.. _mixing:
|
|
|
|
|
|
Mixing
|
|
------
|
|
|
|
In some cases a mixing of two consecutive self energies (or alternatively two hybridization
|
|
functions) can be necessary in order to ensure convergence::
|
|
|
|
mix = 0.8 # mixing factor
|
|
if (iteration_number>1 or previous_present):
|
|
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)
|
|
|
|
In this little piece of code, which should be placed after calling the solver, two consecutive
|
|
self energies are linearly mixed with the factor :emphasis:`mix`. Of course, it is possible
|
|
to implement more advanced mixing schemes (e.g. Broyden's methods), however, in most cases
|
|
simple linear mixing or even no mixing is sufficient for a reasonably fast convergence.
|