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168 lines
7.3 KiB
ReStructuredText
168 lines
7.3 KiB
ReStructuredText
.. highlight:: python
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.. _singleshot:
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Single-shot DFT+DMFT
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====================
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After having set up the hdf5 archive, we can now proceed to our first DFT+DMFT calculation.
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It consists of initialization steps, and the actual DMFT self-consistency loop,
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With the code snippets below you can build your own script and target
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it to your needs. Little examples on :ref:`mixing <mixing>` and on
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:ref:`restarting from a previous calculation <restartcalc>` at the end of this page
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should also demonstrate how simple you can modify your own DMFT script. A full working
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calculation for SrVO3 is discussed in the :ref:`next section <SrVO3>`.
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Initialization of the calculation
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---------------------------------
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Before doing the actual calculation, we have to initialize all needed objects.
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The first thing is the :class:`SumkDFT <dft.sumk_dft.SumkDFT>` class.
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It contains all basic routines that are necessary to perform a summation in k-space
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to get the local quantities used in DMFT. It is initialized by::
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from pytriqs.applications.dft.sumk_dft import *
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SK = SumkDFT(hdf_file = filename + '.h5')
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Setting up the impurity solver
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------------------------------
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The next step is to setup an impurity solver. There are different
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solvers available within the :ref:`TRIQS <triqslibs:welcome>` framework.
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E.g. for :ref:`SrVO3 <SrVO3>`, we will use the hybridization
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expansion :ref:`CTHYB solver <triqscthyb:welcome>`. Later on, we will
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see also the example of the `Hubbard-I solver <https://triqs.ipht.cnrs.fr/1.x/applications/hubbardI/>`_.
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They all have in common, that they are called by an uniform command::
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S.solve(params)
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where :emphasis:`params` are the solver parameters and depend on the actual
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solver. Setting up the :ref:`CTHYB solver <triqscthyb:welcome>` for SrVO3 is
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discussed on the :ref:`next page <SrVO3>`. Here, let us now perform the DMFT
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loop using the methods of :program:`DFTTools`, assuming that we have already
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set up a working solver instance.
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Doing the DMFT loop
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-------------------
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Having initialized the :class:`Sumk class <dft.sumk_dft.SumkDFT>`
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and the solver, we can proceed with the actual DMFT part of the calculation.
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We set up the loop over DMFT iterations and the self-consistency condition::
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n_loops = 15
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for iteration_number in range(n_loops) : # start the DMFT loop
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SK.set_Sigma([ S.Sigma ]) # Put self energy to the SumK class
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chemical_potential = SK.calc_mu() # calculate the chemical potential for the given density
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S.G_iw << SK.extract_G_loc()[0] # extract the local Green function
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S.G0_iw << inverse(S.Sigma_iw + inverse(S.G_iw)) # finally get G0, the input for the solver
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S.solve(h_int=h_int, **p) # now solve the impurity problem
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dm = S.G_iw.density() # Density matrix of the impurity problem
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SK.calc_dc(dm, U_interact=U, J_hund=J, orb=0, use_dc_formula=1) # Set the double counting term
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SK.save(['chemical_potential','dc_imp','dc_energ']) # Save data in the hdf5 archive
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These steps are enough for a basic DMFT Loop.
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After the self-consistency steps, which lead to a new :math:`G^0(i\omega)`,
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the impurity solver is called. Different to model calculations, we have to do a few
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more steps after this, because of the double-counting correction. We first
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calculate the density of the impurity problem. Then, the routine :meth:`calc_dc <dft.sumk_dft.SumkDFT.calc_dc>`
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takes as parameters this density matrix, the Coulomb interaction, Hund's rule
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coupling, and the type of double-counting that should be used. Possible values
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for :emphasis:`use_dc_formula` are:
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* `0`: Full-localised limit (FLL)
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* `1`: DC formula as given in K. Held, Adv. Phys. 56, 829 (2007).
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* `2`: Around-mean-field (AMF)
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At the end of the calculation, we can save the Greens function and self energy into a file::
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from pytriqs.archive import HDFArchive
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import pytriqs.utility.mpi as mpi
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if mpi.is_master_node():
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ar = HDFArchive("YourDFTDMFTcalculation.h5",'w')
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ar["G"] = S.G_iw
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ar["Sigma"] = S.Sigma_iw
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These are the essential steps necessary for a one-shot DFT+DMFT calculation.
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For a detailed description of the :class:`SumkDFT <dft.sumk_dft.SumkDFT>`
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routines, see the :ref:`reference manual <reference>`. To perform full charge self-consistent calculations, there
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are some more things to consider, which we will see :ref:`later on <full_charge_selfcons>`.
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.. _restartcalc:
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Restarting a calculation
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------------------------
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Often only a few DMFT iterations are performed first, and thus, it is desirable to
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carry out further iterations, e.g. to improve on the convergence. With a little modification
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at the initialization stage (before the DMFT loop) it is possible to detect if previous runs
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are present, or if the calculation should start from scratch::
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previous_runs = 0
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previous_present = False
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if mpi.is_master_node():
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f = HDFArchive(dft_filename+'.h5','a')
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if 'dmft_output' in f:
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ar = f['dmft_output']
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if 'iterations' in ar:
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previous_present = True
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previous_runs = ar['iterations']
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else:
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f.create_group('dmft_output')
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del f
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previous_runs = mpi.bcast(previous_runs)
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previous_present = mpi.bcast(previous_present)
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You can see from this code snippet, that removing the subgroup :emphasis:`dmft_results` from the
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hdf file has the effect of reseting the calculation to the starting point. If there are previous
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runs stored in the hdf5 archive, we can now load the self energy, the chemical potential and
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double counting values of the last iteration::
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if previous_present:
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if mpi.is_master_node():
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ar = HDFArchive(dft_filename+'.h5','a')
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S.Sigma_iw << ar['dmft_output']['Sigma_iw']
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del ar
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S.Sigma_iw << mpi.bcast(S.Sigma_iw)
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chemical_potential,dc_imp,dc_energ = SK.load(['chemical_potential','dc_imp','dc_energ'])
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SK.set_mu(chemical_potential)
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SK.set_dc(dc_imp,dc_energ)
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The data is loaded only on the master node, and therefore we broadcast it to the slave nodes.
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Be careful when storing the :emphasis:`iteration_number` as we also have to add the previous
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iteration count::
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ar['dmft_output']['iterations'] = iteration_number + previous_runs
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.. _mixing:
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Mixing
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------
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In some cases a mixing of two consecutive self energies (or alternatively two hybridization
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functions) can be necessary in order to ensure convergence::
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mix = 0.8 # mixing factor
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if (iteration_number>1 or previous_present):
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if mpi.is_master_node():
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ar = HDFArchive(dft_filename+'.h5','a')
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mpi.report("Mixing Sigma and G with factor %s"%mix)
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S.Sigma_iw << mix * S.Sigma_iw + (1.0-mix) * ar['dmft_output']['Sigma_iw']
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S.G_iw << mix * S.G_iw + (1.0-mix) * ar['dmft_output']['G_iw']
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del ar
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S.G_iw << mpi.bcast(S.G_iw)
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S.Sigma_iw << mpi.bcast(S.Sigma_iw)
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In this little piece of code, which should be placed after calling the solver, two consecutive
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self energies are linearly mixed with the factor :emphasis:`mix`. Of course, it is possible
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to implement more advanced mixing schemes (e.g. Broyden's methods), however, in most cases
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simple linear mixing or even no mixing is sufficient for a reasonably fast convergence.
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