.. _analysis: Tools for analysis ================== This section explains how to use some tools of the package in order to analyse the data. There are two practical tools for which a self energy on the real axis is not needed, namely: * :meth:`dos_wannier_basis ` for the density of states of the Wannier orbitals and * :meth:`partial_charges ` for the partial charges according to the :program:`Wien2k` definition. However, a real frequency self energy has to be provided by the user for the methods: * :meth:`dos_parproj_basis ` for the momentum-integrated spectral function including self energy effects and * :meth:`spaghettis ` for the momentum-resolved spectral function (i.e. ARPES) .. warning:: This package does NOT provide an explicit method to do an **analytic continuation** of the self energies and Green functions from Matsubara frequencies to the real frequency axis! There are methods included e.g. in the :program:`ALPS` package, which can be used for these purposes. Keep in mind that all these methods have to be used very carefully! Initialisation -------------- All tools described below are collected in an extension of the :class:`SumkDFT ` class and are loaded by importing the module :class:`SumkDFTTools `:: from pytriqs.applications.dft.sumk_dft_tools import * The initialisation of the class is equivalent to that of the :class:`SumkDFT ` class:: SK = SumkDFTTools(hdf_file = filename + '.h5') Note that all routines available in :class:`SumkDFT ` are also available here. If required, we have to load and initialise the real frequency self energy. Most conveniently, you have your self energy already stored as a real frequency :class:`BlockGf ` object in a hdf5 file:: ar = HDFArchive('case.h5', 'a') SigmaReFreq = ar['dmft_output']['Sigma_w'] You may also have your self energy stored in text files. For this case we provide the function :meth:`constr_Sigma_real_axis`, which loads the data and puts it into a real frequency :class:`BlockGf ` object:: from pytriqs.applications.dft.build_sigma_from_txt import * SigmaReFreq = constr_Sigma_real_axis(SK, filename, hdf=False, hdf_dataset='SigmaReFreq',n_om=0, orb=0) where: * `filename`: the name of the hdf5 archive file or the `fname` pattern in text files names as described above, * `hdf`: if `True`, the real axis self energy will be read from the hdf5 file, otherwise from the text files, * `hdf_dataset`: the name of dataset where the self energy is stored in the hdf5 file, * `orb`: index of an inequivalent shell, * `n_om`: the number of points in the real-axis mesh (used only if `hdf=False`). It is important that you follow some rules concerning the structure of your data files: * Each data file should contain three columns: real frequency, real part and imaginary part of the self energy exactly in this order. * If all blocks of your self energy are of dimension 1x1, you store them in `filename_(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 zero based orbital indices, in the `filename_(block)` directory. Finally, we put the self energy into the `SK` object:: SK.put_Sigma(Sigma_imp = [SigmaReFreq]) and additionally set the chemical potential and the double counting correction from the DMFT calculation:: chemical_potential, dc_imp, dc_energ = SK.load(['chemical_potential','dc_imp','dc_energ']) SK.set_mu(chemical_potential) SK.set_dc(dc_imp,dc_energ) del ar .. _dos_wannier: Density of states of the Wannier orbitals ----------------------------------------- For plotting the density of states of the Wannier orbitals, you type:: SK.dos_wannier_basis(broadening=0.03, mesh=[om_min, om_max, n_om], with_Sigma=False, with_dc=False, save_to_file=True) which produces plots between the real frequencies `om_min` and `om_max`, using a mesh of `n_om` points. The parameter `broadening` defines an additional Lorentzian broadening, and has the default value of `0.01 eV`. To check the Wannier density of states after the projection set `with_Sigma` and `with_dc` to `False`. If `save_to_file` is set to `True` the output is printed into the files * `DOS_wannier_(sp).dat`: The total DOS, where `(sp)` stands for `up`, `down`, or combined `ud`. The latter case is relevant for calculations including spin-orbit interaction. * `DOS_wannier_(sp)_proj(i).dat`: The DOS projected to an orbital with index `(i)`. The index `(i)` refers to the indices given in ``SK.shells``. * `DOS_wannier_(sp)_proj(i)_(m)_(n).dat`: As above, but printed as orbitally-resolved matrix in indices `(m)` and `(n)`. For `d` orbitals, it gives the DOS separately for, e.g., :math:`d_{xy}`, :math:`d_{x^2-y^2}`, and so on, otherwise, the ouptput is returned by the function for a further usage in :program:`python`. Partial charges --------------- Since we can calculate the partial charges directly from the Matsubara Green's functions, we also do not need a real frequency self energy for this purpose. The calculation is done by:: SK.put_Sigma(Sigma_imp = SigmaImFreq) dm = SK.partial_charges(beta=40.0, with_Sigma=True, with_dc=True) which calculates the partial charges using the self energy, double counting, and chemical potential as set in the `SK` object. On return, `dm` is a list, where the list items correspond to the density matrices of all shells defined in the list `SK.shells`. This list is constructed by the :program:`Wien2k` converter routines and stored automatically in the hdf5 archive. For the structure of `dm`, see also :meth:`reference manual `. Correlated spectral function (with real frequency self energy) -------------------------------------------------------------- To produce both the momentum-integrated (total density of states or DOS) and orbitally-resolved (partial/projected DOS) spectral functions we can execute:: SK.dos_parproj_basis(broadening=0.0, with_Sigma=True, with_dc=True, save_to_file=True) The variable `broadening` is an additional Lorentzian broadening (default: `0.01 eV`) applied to the resulting spectra. The output is written in the same way as described above for the :ref:`Wannier density of states `, but with filenames `DOS_parproj_*` instead. Momentum resolved spectral function (with real frequency self energy) --------------------------------------------------------------------- Another quantity of interest is the momentum-resolved spectral function, which can directly be compared to ARPES experiments. First we have to execute `lapw1`, `lapw2 -almd` and :program:`dmftproj` with the `-band` option and use the :meth:`convert_bands_input ` routine, which converts the required files (for a more detailed description see :ref:`conversion`). The spectral function is then calculated by typing:: SK.spaghettis(broadening=0.01,plot_shift=0.0,plot_range=None,ishell=None,save_to_file='Akw_') Here, optional parameters are * `shift`: An additional shift added as `(ik-1)*shift`, where `ik` is the index of the `k` point. This is useful for plotting purposes. The default value is 0.0. * `plotrange`: A list with two entries, :math:`\omega_{min}` and :math:`\omega_{max}`, which set the plot range for the output. The default value is `None`, in which case the full momentum range as given in the self energy is used. * `ishell`: An integer denoting the orbital index `ishell` onto which the spectral function is projected. The resulting function is saved in the files. The default value is `None`. Note for experts: The spectra are not rotated to the local coordinate system used in :program:`Wien2k`. The output is written as the 3-column files ``Akw(sp).dat``, where `(sp)` is defined as above. The output format is `k`, :math:`\omega`, `value`.