.. _Sr2MgOsO6_noSOC: Here we will discuss a calculation where off-diagonal matrix elements show up, and will discuss step-by-step how this calculation can be set up. The full script for this calculation is also provided here (:download:`dft_dmft_cthyb.py `). Note that we do not include spin-orbit coupling here for pedagogical reasons. For the real material it is necessary to include also SOC. 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:`Sr2MgOs6_noSOC.struct`. We use the following: .. literalinclude:: images_scripts/Sr2MgOsO6_noSOC.struct The DFT calculation is done as usual, for instance you can use for the initialisation init -b -vxc 5 -numk 2000 This is setting up a non-magnetic calculation, using the LDA and 2000 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. We use the same input file for :program:`dmftproj` as it was used in the :ref:`documentation`: .. literalinclude:: images_scripts/Sr2MgOsO6_noSOC.indmftpr Note that, due to the distortions in the crystal structure, we need to include all five d orbitals in the calculation (line 8 in the input file above). To prepare the input data for :program:`dmftproj` we 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 `. A simple python script that initialises the converter is:: from triqs_dft_tools.converters.wien2k_converter import * Converter = Wien2kConverter(filename = "Sr2MgOsO6_noSOC") 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:`Sr2MgOsO6_noSOC.h5`. [CONTINUE HERE] 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 pytriqs.gf import * from pytriqs.archive import HDFArchive from pytriqs.operators.util import * from triqs_cthyb import * import pytriqs.utility.mpi as mpi The last two lines load the modules for the construction of the :ref:`CTHYB solver `. 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 ` 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 ` 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 ` 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 `. The next step is to initialize the :class:`solver class `. 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 ` library:: n_orb = SK.corr_shells[0]['dim'] l = SK.corr_shells[0]['l'] spin_names = ["up","down"] orb_names = [i for i in range(n_orb)] # Use GF structure determined by DFT blocks: gf_struct = [(block, indices) for block, indices in SK.gf_struct_solver[0].iteritems()] # 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 ` library. 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 `, 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,orb=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()) # Init the DC term and the real part of Sigma, if no previous runs found: if (iteration_number==1 and previous_present==False): 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 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) # Write the final Sigma and G to the hdf5 archive: if mpi.is_master_node(): with HDFArchive(dft_filename+'.h5','a') 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 ` is part of the :ref:`TRIQS ` 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`.