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120 lines
6.1 KiB
ReStructuredText
120 lines
6.1 KiB
ReStructuredText
.. _analysis:
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Tools for analysis
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==================
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This section explains how to use some tools of the package in order to analyse the data.
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.. warning::
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The package does NOT provide an explicit method to do an **analytic continuation** of the
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self energies and Green functions from Matsubara frequencies to the real frequancy axis!
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There are methods included e.g. in the :program:`ALPS` package, which can be used for these purposes. But
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be careful: All these methods have to be used very carefully!
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The tools for analysis can be found in an extension of the :class:`SumkLDA` class and are
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loaded by importing the module :class:`SumkLDATools`::
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from pytriqs.applications.dft.sumk_lda_tools import *
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There are two practical tools for which you do not need a self energy on the real axis, namely the:
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* density of states of the Wannier orbitals,
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* partial charges according to the Wien2k definition.
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The self energy on the real frequency axis is necessary in computing the:
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* momentum-integrated spectral function including self-energy effects,
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* momentum-resolved spectral function (i.e. ARPES).
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The initialisation of the class is equivalent to that of the :class:`SumkLDA`
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class::
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SK = SumkLDATools(hdf_file = filename)
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Note that all routines available in :class:`SumkLDA` are also available here.
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Routines without real-frequency self energy
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-------------------------------------------
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For plotting the
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density of states of the Wannier orbitals, you simply type::
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SK.check_input_dos(om_min, om_max, n_om)
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which produces plots between the real frequencies `om_min` and `om_max`, using a mesh of `n_om` points. There
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is an optional parameter `broadening` which defines an additional Lorentzian broadening, and has the default value of
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`0.01` by default.
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Since we can calculate the partial charges directly from the Matsubara Green's functions, we also do not need a
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real-frequency self energy for this purpose. The calculation is done by::
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ar = HDFArchive(SK.hdf_file)
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SK.put_Sigma([ ar['SigmaImFreq'] ])
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del ar
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dm = SK.partial_charges()
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which calculates the partial charges using the data stored in the hdf5 file, namely the self energy, double counting, and
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chemical potential. Here we assumed that the final self energy is stored as `SigmaImFreq` in the archive.
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On return, `dm` is a list, where the list items correspond to the density matrices of all shells
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defined in the list `SK.shells`. This list is constructed by the Wien2k converter routines and stored automatically
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in the hdf5 archive. For the detailed structure of `dm`, see the reference manual.
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Routines with real-frequency self energy
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----------------------------------------
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In order to plot data including correlation effects on the real axis, one has to provide the real frequency self energy.
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Most conveniently, it is stored as a real frequency :class:`BlockGf` object in the hdf5 file::
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ar = HDFArchive(filename+'.h5','a')
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ar['SigmaReFreq'] = SigmaReFreq
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del ar
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You may also store it in text files. If all blocks of your self energy are of dimension 1x1, you store them in `fname_(block)0.dat` files. Here `(block)` is a block name (`up`, `down`, or combined `ud`). In the case when you have matrix blocks, you store them in `(i)_(j).dat` files, where `(i)` and `(j)` are the orbital indices, in the `fname_(block)` directory.
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This self energy is loaded and put into the :class:`SumkLDA` class by the function::
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SK.constr_Sigma_real_axis(filename, hdf=True, hdf_dataset='SigmaReFreq',n_om=0)
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where:
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* `filename`: the name of the hdf5 archive file or the `fname` pattern in text files names as described above,
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* `hdf`: if `True`, the real-axis self energy will be read from the hdf5 file, otherwise from the text files,
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* `hdf_dataset`: the name of dataset where the self energy is stored in the hdf5 file,
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* `n_om`: the number of points in the real-axis mesh (used only if `hdf=False`).
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The chemical potential as well as the double counting correction were already read in the initialisation process.
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With this self energy, we can now execute::
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SK.dos_partial(broadening=broadening)
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This produces both the momentum-integrated (total density of states or DOS) and orbitally-resolved (partial/projected DOS) spectral functions.
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The variable `broadening` is an additional Lorentzian broadening applied to the resulting spectra.
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The output is printed into the files
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* `DOScorr(sp).dat`: The total DOS, where `(sp)` stands for `up`, `down`, or combined `ud`. The latter case
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is relevant for calculations including spin-orbit interaction.
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* `DOScorr(sp)_proj(i).dat`: The DOS projected to an orbital with index `(i)`. The index `(i)` refers to
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the indices given in ``SK.shells``.
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* `DOScorr(sp)_proj(i)_(m)_(n).dat`: As above, but printed as orbitally-resolved matrix in indices
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`(m)` and `(n)`. For `d` orbitals, it gives the DOS seperately for, e.g., :math:`d_{xy}`, :math:`d_{x^2-y^2}`, and so on.
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Another quantity of interest is the momentum-resolved spectral function, which can directly be compared to ARPES
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experiments. We assume here that we already converted the output of the :program:`dmftproj` program with the
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converter routines (see :ref:`interfacetowien`). The spectral function is calculated by::
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SK.spaghettis(broadening)
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Optional parameters are
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* `shift`: An additional shift added as `(ik-1)*shift`, where `ik` is the index of the `k` point. This is useful for plotting purposes.
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The default value is 0.0.
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* `plotrange`: A list with two entries, :math:`\omega_{min}` and :math:`\omega_{max}`, which set the plot
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range for the output. The default value is `None`, in which case the full momentum range as given in the self energy is used.
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* `ishell`: An integer denoting the orbital index `ishell` onto which the spectral function is projected. The resulting function is saved in
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the files. The default value is `None`. Note for experts: The spectra are not rotated to the local coordinate system used in :program:`Wien2k`.
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The output is written as the 3-column files ``Akw(sp).dat``, where `(sp)` is defined as above. The output format is
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`k`, :math:`\omega`, `value`.
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