mirror of https://github.com/triqs/dft_tools
292 lines
12 KiB
ReStructuredText
292 lines
12 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 do our DFT+DMFT calculation. It consists of
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initialization steps, and the actual DMFT self-consistency loop, as is
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discussed below.
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Initialisation of the calculation
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---------------------------------
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Before doing the calculation, we have to intialize all the objects that we will need. The first thing is the
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:class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>` class. 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. Below, we will discuss
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the example of the hybridisation
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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. They all have in common,
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that they are called by a uniform command::
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S.solve(params)
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where `params` are the solver parameters and depend on the actual
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solver that is used. Before going into the details of the solver, let
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us discuss in the next section how to perform the DMFT loop using
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the methods of :program:`dft_tools`, assuming that we have set up a
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working solver instance.
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Doing the DMFT loop
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-------------------
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Having initialized the SumK class and the Solver, we can proceed with the DMFT
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loop itself. We have to set up the loop over DMFT
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iterations and the self-consistency condition::
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n_loops = 5
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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 basic steps are enough to set up the basic DMFT Loop. For a detailed
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description of the :class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>` routines, see the reference
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manual.
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After
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the self-consistency steps (extracting a new :math:`G^0(i\omega)`),
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the Anderson impurity problem is solved.
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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 `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 `use_dc_formula` are:
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* `0`: Full-localised limit
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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
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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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This is it!
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These are the essential steps to do a one-shot DFT+DMFT calculation.
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For full charge-self consistent calculations, there are some more things
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to consider, which we will see later on.
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A full DFT+DMFT calculation
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---------------------------
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We will discuss now how to set up a full working calculation,
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including setting up the CTHYB solver, and specifying some more parameters
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in order to make the calculation more efficient. Here, we
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will see a more advanced example, which is also suited for parallel
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execution. For the convenience of the user, we provide also two
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working python scripts in this documentation. One for a calculation
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using Kanamori definitions (:download:`dft_dmft_cthyb.py
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<images_scripts/dft_dmft_cthyb.py>`) and one with a
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rotational-invariant Slater interaction hamiltonian (:download:`dft_dmft_cthyb_slater.py
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<images_scripts/dft_dmft_cthyb.py>`). The user has to adapt these
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scripts to his own needs.
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First, we load the necessary modules::
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from pytriqs.applications.dft.sumk_dft import *
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from pytriqs.gf.local import *
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from pytriqs.archive import HDFArchive
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from pytriqs.operators.util import *
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from pytriqs.applications.impurity_solvers.cthyb import *
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The last two lines load the modules for the construction of the CTHYB
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solver.
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Then we define some parameters::
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dft_filename='SrVO3'
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U = 4.0
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J = 0.65
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beta = 40
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loops = 10 # Number of DMFT sc-loops
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sigma_mix = 0.8 # Mixing factor of Sigma after solution of the AIM
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dc_type = 1 # DC type: 0 FLL, 1 Held, 2 AMF
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use_blocks = True # use bloc structure from DFT input
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prec_mu = 0.0001
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# Solver parameters
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p = {}
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p["length_cycle"] = 200
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p["n_warmup_cycles"] = 2000
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p["n_cycles"] = 20000
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Most of these parameters are self-explanatory. The first,
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`dft_filename`, gives the filename of the input files. For more
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details on the solver parameters, we refer the user to
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the :ref:`CTHYB solver <triqscthyb:welcome>` documentation.
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We assume that the conversion to the hdf5 archive is already done. We
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can check now in this archive, if previous runs are present, or if we have to start
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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 in this code snipet, that all results of this calculation
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will be stored in a separate subgroup in the hdf5 file, called
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`dmft_output`. Removing this subgroup allows you to reset your
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calculation to the starting point easily.
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Now we can use all this information to initialise the :class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>` class::
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SK = SumkDFT(hdf_file=dft_filename+'.h5',use_dft_blocks=use_blocks)
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The next step is to initialise the :class:`Solver <pytriqs.applications.impurity_solvers.cthyb.Solver>` class. It consist
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of two steps
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#. Calculating the multi-band interaction matrix, and setting up the
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interaction hamiltonian
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#. Setting up the solver class
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The first step is done using methods of
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the :ref:`TRIQS <triqslibs:welcome>` library::
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n_orb = SK.corr_shells[0]['dim']
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l = SK.corr_shells[0]['l']
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spin_names = ["up","down"]
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orb_names = [i for i in range(n_orb)]
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# Use GF structure determined by DFT blocks:
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gf_struct = SK.gf_struct_solver[0]
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# Construct U matrix for density-density calculations:
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Umat, Upmat = U_matrix_kanamori(n_orb=n_orb, U_int=U, J_hund=J)
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We assumed here that we want to use an interaction matrix with
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Kanamori definitions of :math:`U` and :math:`J`. For
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other choices (Slater interaction matrix for instance), and other
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parameters, we refer to the reference manual
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of the :ref:`TRIQS <triqslibs:welcome>` library.
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Next, we construct the hamiltonian and the solver::
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h_int = h_int_density(spin_names, orb_names, map_operator_structure=SK.sumk_to_solver[0], U=Umat, Uprime=Upmat)
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S = Solver(beta=beta, gf_struct=gf_struct)
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As you see, we take only density-density interactions into
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account. Other choices for the hamiltonian are
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* h_int_kanamori
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* h_int_slater
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These two include full rotational invariant interactions. Again,
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options can be found in the :ref:`TRIQS <triqslibs:welcome>` library
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reference manual.
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If there are previous runs stored in the hdf5 archive, we can now load the self energy
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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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chemical_potential,dc_imp,dc_energ = SK.load(['chemical_potential','dc_imp','dc_energ'])
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S.Sigma_iw << mpi.bcast(S.Sigma_iw)
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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 self-energy is broadcast from the master node to the slave nodes. Also, the
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last saved chemical potential and double counting values are read in and set.
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Now we can go to the definition of the self-consistency step. It consists again
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of the basic steps discussed in the previous section, with some additional
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refinements::
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for iteration_number in range(1,loops+1):
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if mpi.is_master_node(): print "Iteration = ", iteration_number
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SK.symm_deg_gf(S.Sigma_iw,orb=0) # symmetrise Sigma
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SK.set_Sigma([ S.Sigma_iw ]) # put Sigma into the SumK class
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chemical_potential = SK.calc_mu( precision = prec_mu ) # find the chemical potential for given density
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S.G_iw << SK.extract_G_loc()[0] # calc the local Green function
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mpi.report("Total charge of Gloc : %.6f"%S.G_iw.total_density())
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# Init the DC term and the real part of Sigma, if no previous runs found:
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if (iteration_number==1 and previous_present==False):
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dm = S.G_iw.density()
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SK.calc_dc(dm, U_interact = U, J_hund = J, orb = 0, use_dc_formula = dc_type)
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S.Sigma_iw << SK.dc_imp[0]['up'][0,0]
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# Calculate new G0_iw to input into the solver:
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S.G0_iw << S.Sigma_iw + inverse(S.G_iw)
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S.G0_iw << inverse(S.G0_iw)
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# Solve the impurity problem:
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S.solve(h_int=h_int, **p)
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# Solved. Now do post-solution stuff:
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mpi.report("Total charge of impurity problem : %.6f"%S.G_iw.total_density())
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# Now mix Sigma and G with factor sigma_mix, if wanted:
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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"%sigma_mix)
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S.Sigma_iw << sigma_mix * S.Sigma_iw + (1.0-sigma_mix) * ar['dmft_output']['Sigma_iw']
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S.G_iw << sigma_mix * S.G_iw + (1.0-sigma_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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# Write the final Sigma and G to the hdf5 archive:
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if mpi.is_master_node():
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ar = HDFArchive(dft_filename+'.h5','a')
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ar['dmft_output']['iterations'] = iteration_number + previous_runs
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ar['dmft_output']['G_0'] = S.G0_iw
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ar['dmft_output']['G_tau'] = S.G_tau
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ar['dmft_output']['G_iw'] = S.G_iw
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ar['dmft_output']['Sigma_iw'] = S.Sigma_iw
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del ar
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# Set the new double counting:
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dm = S.G_iw.density() # compute the 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 = dc_type)
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# Save stuff into the dft_output group of hdf5 archive in case of rerun:
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SK.save(['chemical_potential','dc_imp','dc_energ'])
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This is all we need for the DFT+DMFT calculation. At the end, all results are stored in the hdf5 output file.
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