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225 lines
9.1 KiB
ReStructuredText
225 lines
9.1 KiB
ReStructuredText
.. _SrVO3:
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SrVO3 (single-shot)
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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 the initialization of the :ref:`CTHYB solver <triqscthyb:welcome>`.
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Some additional parameter are introduced to make the calculation
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more efficient. This is a more advanced example, which is
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also suited for parallel execution. The conversion, which
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we assume to be carried out already, is discussed :ref:`here <conversion>`.
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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_slater.py>`). The user has to adapt these
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scripts to his own needs. How to execute your script is described :ref:`here<runpy>`.
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Loading modules
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---------------
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First, we load the necessary modules::
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from triqs_dft_tools.sumk_dft import *
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from pytriqs.gf import *
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from pytriqs.archive import HDFArchive
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from pytriqs.operators.util import *
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from triqs_cthyb import *
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import pytriqs.utility.mpi as mpi
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The last two lines load the modules for the construction of the
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:ref:`CTHYB solver <triqscthyb:welcome>`.
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Initializing SumkDFT
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--------------------
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We define some parameters, which should be self-explanatory::
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dft_filename = 'SrVO3' # filename
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U = 4.0 # interaction parameters
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J = 0.65
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beta = 40 # inverse temperature
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loops = 15 # number of DMFT loops
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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 # precision of chemical potential
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And next, we can initialize the :class:`SumkDFT <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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Initializing the solver
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-----------------------
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We also have to specify the :ref:`CTHYB solver <triqscthyb:welcome>` related settings.
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We assume that the DMFT script for SrVO3 is executed on 16 cores. A sufficient set
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of parameters for a first guess is::
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p = {}
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# solver
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p["random_seed"] = 123 * mpi.rank + 567
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p["length_cycle"] = 200
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p["n_warmup_cycles"] = 100000
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p["n_cycles"] = 1000000
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# tail fit
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p["perform_tail_fit"] = True
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p["fit_max_moment"] = 4
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p["fit_min_n"] = 30
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p["fit_max_n"] = 60
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Here we use a tail fit to deal with numerical noise of higher Matsubara frequencies.
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For other options and more 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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It is important to note that the solver parameters have to be adjusted for
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each material individually. A guide on how to set the tail fit parameters is given
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:ref:`below <tailfit>`.
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The next step is to initialize the
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:class:`solver class <triqs_cthyb.Solver>`.
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It consist of two parts:
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#. Calculating the multi-band interaction matrix, and constructing the
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interaction Hamiltonian.
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#. Initializing the solver class itself.
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The first step is done using methods of 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 = [(block, indices) for block, indices in SK.gf_struct_solver[0].iteritems()]
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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`.
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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 Hamiltonians with, e.g. with full rotational invariant interactions are:
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* h_int_kanamori
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* h_int_slater
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For other choices of the interaction matrices (e.g Slater representation) or
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Hamiltonians, we refer to the reference manual of the :ref:`TRIQS <triqslibs:welcome>`
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library.
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DMFT cycle
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----------
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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 :ref:`previous section <singleshot>`, with
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some additional 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) # symmetrizing 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 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"%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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# 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
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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 user_data 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.
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You can see in this code snippet, that all results of this calculation
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will be stored in a separate subgroup in the hdf5 file, called `dmft_output`.
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Note that this script performs 15 DMFT cycles, but does not check for
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convergence. Of course, it would be possible to build in convergence criteria.
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A simple check for convergence can be also done if you store multiple quantities
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of each iteration and analyse the convergence by hand. In general, it is advisable
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to start with a lower statistics (less measurements), but then increase it at a
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point close to converged results (e.g. after a few initial iterations). This helps
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to keep computational costs low during the first iterations.
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Using the Kanamori Hamiltonian and the parameters above (but on 16 cores),
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your self energy after the **first iteration** should look like the
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self energy shown below.
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.. image:: images_scripts/SrVO3_Sigma_iw_it1.png
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:width: 700
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:align: center
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.. _tailfit:
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Tail fit parameters
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-------------------
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A good way to identify suitable tail fit parameters is by "human inspection".
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Therefore disabled the tail fitting first::
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p["perform_tail_fit"] = False
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and perform only one DMFT iteration. The resulting self energy can be tail fitted by hand::
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Sigma_iw_fit = S.Sigma_iw.copy()
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Sigma_iw_fit << tail_fit(S.Sigma_iw, fit_max_moment = 4, fit_min_n = 40, fit_max_n = 160)[0]
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Plot the self energy and adjust the tail fit parameters such that you obtain a
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proper fit. The :meth:`fit_tail function <pytriqs.gf.tools.tail_fit>` is part
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of the :ref:`TRIQS <triqslibs:welcome>` library.
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For a self energy which is going to zero for :math:`i\omega \rightarrow 0` our suggestion is
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to start the tail fit (:emphasis:`fit_min_n`) at a Matsubara frequency considerable above the minimum
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of the self energy and to stop (:emphasis:`fit_max_n`) before the noise fully takes over.
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If it is difficult to find a reasonable fit in this region you should increase
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your statistics (number of measurements). Keep in mind that :emphasis:`fit_min_n`
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and :emphasis:`fit_max_n` also depend on :math:`\beta`.
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