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[doc] Restructured parts of the user guide

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* New page on: What you should know
    * SrVO3 DMFT separated from single-shot page
    * section on tailfit, mixing and restarting calcs
    * correcting typos
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What you should know
====================
Probably, you can hardly wait to perform your first DFT+DMFT calculation
with the :program:`DFTTools` package. This documentation and user guide
should make it as easy as possible to get started quickly.
However, it is mutually important to sort out a few prerequisites first.
What is :program:`DFTTools`?
----------------------------
:program:`DFTTools` connects the :ref:`TRIQS <triqslibs:welcome>` library
to realistic materials calculations based
on density functional theory (DFT). It allows an efficient implementation
of DFT plus dynamical mean-field theory (DMFT) calculations and it supplies
tools and methods to construct Wannier functions and to perform the
DMFT self-consistency cycle in this basis set. Post-processing tools,
such as band-structure plotting or the calculation of transport properties
are also implemented. The package comes with a fully charge self-consistent
interface to the Wien2k band structure code, as well as a generic interface.
We assume that you are already know about DFT and the usage of Wien2k.
Have a look at :ref:`DFT+DMFT page <dftplusdmft>` for a brief introduction on
the DFT+DMFT method and on how the theory is reflected in the
:ref:`basic structure <structure>` of the :program:`DFTTools` package.
Understand the philosophy of :program:`DFTTools`
------------------------------------------------
The purpose of :program:`DFTTools` is to provide the necessary tools
required for a DFT+DMFT calculations. Putting those tools together to a working
DFT+DMFT implementation is the task of the user. We do not
supply an universal script which runs with the click of a button, simply because
each material requires a different treatment or different settings.
Building your own script offers a great deal of flexibility and customizability.
Additionally, the :ref:`DFTTools user guide <documentation>` is there to support you
during this process.
It should go without saying, but the verification of outputs and the inspection
of results on their meaningfulness is the responsibility of the user.
The :program:`DFTTools` package is a toolbox and **not** a black box!
Learn how to use :ref:`TRIQS <triqslibs:welcome>` (and the :ref:`CTHYB <triqscthyb:welcome>` solver)
----------------------------------------------------------------------------------------------------
As :program:`DFTTools` is a :ref:`TRIQS <triqslibs:welcome>` based application
it is beneficial to invest a few hours to become familiar with
the :ref:`TRIQS <triqslibs:welcome>` basics first. The
`TRIQS tutorial <https://triqs.ipht.cnrs.fr/1.x/tutorials.html>`_ covers
the most important aspects of :ref:`TRIQS <triqslibs:welcome>`. We recommend
downloading our hands-on training in the form of ipython notebooks from
the `tutorials repository on GitHub <https://github.com/TRIQS/tutorials>`_.
Tutorials 1 to 6 are on the :ref:`TRIQS <triqslibs:welcome>` library, whereas tutorials
7 and 8 are more specific to the usage of the :ref:`CTHYB <triqscthyb:welcome>`
hybridization-expansion solver. In general, those tutorials will take at least a full day to finish.
Afterwards you can continue with the :ref:`DFTTools user guide <documentation>`.
Maximum Entropy (MaxEnt)
------------------------
Analytic continuation is needed for many :ref:`post-processing tools <analysis>`, e.g. to
calculate the spectral function, the correlated band structure (:math:`A(k,\omega)`)
and to perform :ref:`transport calculations <Transport>`.
You can use the Pade approximation available in the :ref:`TRIQS <triqslibs:welcome>` library, however,
it turns out to be very unstable for noisy numerical data. Most of the time, the MaxEnt method
is used to obtain data on the real-frequency axis. At the moment neither :ref:`TRIQS <triqslibs:welcome>` nor
:program:`DFTTools` provide such routines.

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@Article{TRIQS/DFTTools,
title = "TRIQS/DFTTools: A \{TRIQS\} application for ab initio calculations of correlated materials ",
journal = "Computer Physics Communications ",
volume = "204",
number = "",
pages = "200 - 208",
year = "2016",
note = "",
issn = "0010-4655",
doi = "http://dx.doi.org/10.1016/j.cpc.2016.03.014",
url = "http://www.sciencedirect.com/science/article/pii/S0010465516300728",
author = "Markus Aichhorn and Leonid Pourovskii and Priyanka Seth and Veronica Vildosola and Manuel Zingl and Oleg E. Peil and Xiaoyu Deng and Jernej Mravlje and Gernot J. Kraberger and Cyril Martins and Michel Ferrero and Olivier Parcollet",
}

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.. _SrVO3:
SrVO3 (single-shot)
===================
We will discuss now how to set up a full working calculation,
including the initialization of the :ref:`CTHYB solver <triqscthyb:welcome>`.
Some additional parameter are introduced to make the calculation
more efficient. This is a more advanced example, which is
also suited for parallel execution. The conversion, which
we assume to be carried out already, is discussed :ref:`here <conversion>`.
For the convenience of the user, we provide also two
working python scripts in this documentation. One for a calculation
using Kanamori definitions (:download:`dft_dmft_cthyb.py
<images_scripts/dft_dmft_cthyb.py>`) and one with a
rotational-invariant Slater interaction Hamiltonian (:download:`dft_dmft_cthyb_slater.py
<images_scripts/dft_dmft_cthyb.py>`). The user has to adapt these
scripts to his own needs.
Loading modules
---------------
First, we load the necessary modules::
from pytriqs.applications.dft.sumk_dft import *
from pytriqs.gf.local import *
from pytriqs.archive import HDFArchive
from pytriqs.operators.util import *
from pytriqs.applications.impurity_solvers.cthyb import *
The last two lines load the modules for the construction of the
:ref:`CTHYB solver <triqscthyb:welcome>`.
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 <dft.sumk_dft.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 <triqscthyb:welcome>` related settings. The
minimal parameters for a SrVO3 DMFT calculation on 16 cores are::
p = {}
# solver
p["random_seed"] = 123 * mpi.rank + 567
p["length_cycle"] = 200
p["n_warmup_cycles"] = 50000
p["n_cycles"] = 500000
# tail fit
p["perform_tail_fit"] = True
p["fit_max_moment"] = 4
p["fit_min_n"] = 60
p["fit_max_n"] = 140
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 <triqscthyb:welcome>` 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 <tailfit>`.
The next step is to initialize the
:class:`solver class <pytriqs.applications.impurity_solvers.cthyb.Solver>`.
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 <triqslibs:welcome>` 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 = SK.gf_struct_solver[0]
# 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 <triqslibs:welcome>`
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 <singleshot>`, 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():
ar = HDFArchive(dft_filename+'.h5','a')
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']
del ar
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():
ar = HDFArchive(dft_filename+'.h5','a')
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
del ar
# 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 is possible to build in convergence criterias.
A simple check for convergence can be also done if you store multiple quantities
of each iteration and analyze 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.
.. _tailfit:
Tail fit paramters
------------------
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::
for name, sig in S.Sigma_iw:
S.Sigma_iw[name].fit_tail(fit_n_moments = 4, fit_min_n = 60, fit_max_n = 140)
Plot the self energy and adjust the tail fit parameters such that you obtain a
proper fit. The :meth:`fit_tail function <pytriqs.gf.local.tools.tail_fit>` is part
of the :ref:`TRIQS <triqslibs:welcome>` 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`.