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[doc] Restructuring doc II
* Committing missing files of last commit
* Correcting typos
* Modifications according to issue #56
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Manuel Zingl
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@ -14,14 +14,16 @@ Olivier Parcollet (CEA Saclay). A first step has been the definition of the
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framework and the construction of the projective Wannier functions as input for
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the DMFT calculations [#dft_tools1]_. This has been followed by the introduction
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of full charge self-consistency [#dft_tools2]_, necessary for total energy
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calculations.
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calculations. The package at hand is fully implemented as an application
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based on the TRIQS library [#dft_tools3]_.
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**Developers**: M. Aichhorn, L. Pourovskii, V. Vildosola, C. Martins, P. Seth, M. Zingl
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**Developers**: M. Aichhorn, L. Pourovskii, P.Seth, V. Vildosola, M. Zingl, O. E. Peil, X. Deng, J. Mravlje, G. Kraberger, C. Martins, M. Ferrero, O. Parcollet
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**Related papers**:
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.. [#dft_tools1] `M. Aichhorn, L. Pourovskii, V. Vildosola, M. Ferrero, O. Parcollet, T. Miyake, A. Georges, and S. Biermann, Phys. Rev. B 80, 085101 (2009) <http://link.aps.org/doi/10.1103/PhysRevB.80.085101>`_ (:download:`bibtex file <dft_tools1.bib>`)
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.. [#dft_tools2] `M. Aichhorn, L. Pourovskii, and A. Georges, Phys. Rev. B 84, 054529 (2011) <http://link.aps.org/doi/10.1103/PhysRevB.84.054529>`_ (:download:`bibtex file <dft_tools2.bib>`)
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.. [#dft_tools3] `M. Aichhorn, L. Pourovskii, P.Seth, V. Vildosola, M. Zingl, O. E. Peil, X. Deng, J. Marvlje, G. Kraberger, C. Martins, M. Ferrero, and O. Parcollet, Commt. Phys. Commun. 204, 200 (2016) <http://www.sciencedirect.com/science/article/pii/S0010465516300728>`_ (:download:`bibtex file <dft_tools3.bib>`)
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This application is a part of our scientific work and we would appreciate if
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projects using it will include a citation to the above relevant papers. In
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@ -1,3 +1,5 @@
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.. _dftplusdmft:
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Introduction to DFT+DMFT
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========================
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@ -8,7 +10,7 @@ terms it states that electrons in a crystal form bands of allowed
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states in momentum space. These states are then filled by the
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electrons according to Pauli's principle up the Fermi level. With this
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simple picture one can explain the electronic band structure of simple
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materials such as elementary copper or aluminium.
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materials such as elementary copper or aluminum.
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Following this principle one can easily classify all existing
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materials into metals and insulators, with semiconductors being
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@ -17,9 +19,8 @@ spectrum. Following this band theory, a system is a metal if there is
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an odd number of electrons in the valence bands, since this leads to a
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partially filled band, cutting the Fermi energy and, thus, producing a
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Fermi surface, i.e metallic behavior. On the other hand, an even
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number of electrons leads to
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completely filled bands with a finite excitation gap to the conduction
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bands, i.e. insulating behavior.
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number of electrons leads to completely filled bands with a finite
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excitation gap to the conduction bands, i.e. insulating behavior.
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This classification works pretty well for a large class of
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materials, where the electronic band structures are reproduced by
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@ -41,7 +42,7 @@ current
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because of the strong Coulomb repulsion between the electrons. With
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reference to Sir Nevill Mott, who contributed substantially to the
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explanation of this effect in the 1930's, these materials are in
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general reffered to as Mott insulators.
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general referred to as Mott insulators.
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Density-functional theory in a (very small) nutshell
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----------------------------------------------------
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@ -63,7 +64,7 @@ that is discussed in the literature on DFT, let us just note that the
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main result of DFT calculations are the Kohn-Sham energies
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:math:`\varepsilon_{\nu\mathbf{k}}` and the Kohn-Sham orbitals :math:`\psi_{\nu\mathbf{k}}(\mathbf{r})`.
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This set of equations is exact, however, the exchange correlation
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potential :math:`V_{xc}(\mathbf{r})` is not known explicitely. In
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potential :math:`V_{xc}(\mathbf{r})` is not known explicitly. In
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order to do actual calculations, it needs to be approximated in some
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way. The local density approximation is one of the most famous
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approximations used in this context. This approximation works well for
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@ -75,7 +76,7 @@ From DFT to DMFT
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In order to extend our calculations to strong correlations, we need to
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go from a description by bands to a description in terms of
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(localised) orbitals: Wannier functions.
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(localized) orbitals: Wannier functions.
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In principle, Wannier functions :math:`\chi_{\mu\sigma}(\mathbf{r})`
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are nothing else than a Fourier transform of the Bloch basis set from
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@ -88,7 +89,7 @@ where we introduced also the spin degree of freedom :math:`\sigma`. The
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unitary matrix :math:`U_{\mu\nu}` is not uniquely defined, but allows for a
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certain amount of freedom in the calculation of Wannier function. A
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very popular choice is the constraint that the resulting Wannier
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functions should be maximally localised in space. Another route,
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functions should be maximally localized in space. Another route,
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computationally much lighter and more stable, are projective Wannier
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functions. This scheme is used for the Wien2k interface in this
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package.
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@ -98,7 +99,7 @@ A central quantity in this scheme is the projection operator
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:math:`\nu` a Bloch band index.
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Its definition and how it is calculated can be found in the original
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literature or in the extensive documentation of the
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:program:`dmftproj` program shipped with :program:`dft_tools`.
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:program:`dmftproj` program shipped with :program:`DFTTools`.
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Using projective Wannier functions for DMFT
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-------------------------------------------
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@ -121,7 +122,7 @@ with the DFT Green function
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This non-interacting Green function :math:`G^0_{mn}(i\omega)` defines,
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together with the interaction Hamiltonian, the Anderson impurity
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model. The DMFT self-consitency cycle can now be formulated as
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model. The DMFT self-consistency cycle can now be formulated as
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follows:
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#. Take :math:`G^0_{mn}(i\omega)` and the interaction Hamiltonian and
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@ -173,9 +174,9 @@ Full charge self-consistency
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The feedback of the electronic correlations to the Kohn-Sham orbitals
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is included by the interacting density matrix. With going into the
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details, it basically consists of calculating the Kohn Sham density
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details, it basically consists of calculating the Kohn-Sham density
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:math:`\rho(\mathbf{r})` in the presence of this interacting density
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matrix. This new density now defines a new Kohn Sham
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matrix. This new density now defines a new Kohn-Sham
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exchange-correlation potential, which in turn leads to new
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:math:`\varepsilon_{\nu\mathbf{k}}`,
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:math:`\psi_{\nu\mathbf{k}}(\mathbf{r})`, and projectors
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@ -186,4 +187,4 @@ step 3, before the local lattice Green
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function is downfolded again into orbital space.
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How all these calculations can be done in practice with this
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:program:`dft_tools` package is subject of the user guide in this documentation.
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:program:`DFTTools` package is subject of the user guide in this documentation.
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@ -1,18 +1,21 @@
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Structure of DFT Tools
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======================
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.. _structure:
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Structure of :program:`DFTTools`
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================================
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.. image:: images/structure.png
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:width: 700
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:align: center
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The central part of :program:`dft_tools`, which is performing the
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The central part of :program:`DFTTools`, which is performing the
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steps for the DMFT self-consistency cycle, is written following the
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same philosophy as the :ref:`TRIQS <triqslibs:welcome>` toolbox. At
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the user level, easy-to-use python modules are provided that allow to
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write simple and short scripts performing the actual
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calculation. Here, we will describe the general structure of the
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package, for the details of how to use the modules, please consult the
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user guide of this :ref:`documentation`.
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write simple and short scripts performing the actual calculation.
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The usage of those modules is presented in the user guide of this
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:ref:`documentation`. Before considering the user guide, we suggest
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to read the following introduction on the general structure of
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the :program:`DFTTools` package.
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The interface layer
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-------------------
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@ -30,37 +33,37 @@ Wien2k interface
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""""""""""""""""
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This interface layer consists of two parts. First, the output from Wien2k
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is taken, and localised Wannier orbitals are constructed. This is done
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by the fortran program :program:`dmftproj`. The second part consist in
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is taken, and localized Wannier orbitals are constructed. This is done
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by the FORTRAN program :program:`dmftproj`. The second part consist in
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the conversion of the :program:`dmftproj` into the hdf5 file
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format to be used for the DMFT calculation. This step is done by a
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python routine called :class:`Wien2kConverter`, that reads the text output and
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creates the hdf5 input file with the necessary ingredients. Quite
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naturally, :program:`dft_tools` will adopt this converter concept also for future
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naturally, :program:`DFTTools` will adopt this converter concept also for future
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developments for other DFT packages.
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General interface
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"""""""""""""""""
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In addition to the specialised Wien2k interface, :program:`dft_tools`
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In addition to the specialized Wien2k interface, :program:`DFTTools`
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provides also a very light-weight general interface. It basically
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consists of a very simple :class:`HkConverter`. As input it requires a
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hamiltonian matrix :math:`H_{mn}(\mathbf{k})` written already in
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localised-orbital indices :math:`m,n`, on a :math:`\mathbf{k}`-point
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Hamiltonian matrix :math:`H_{mn}(\mathbf{k})` written already in
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localized-orbital indices :math:`m,n`, on a :math:`\mathbf{k}`-point
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grid covering the Brillouin zone, and just a few other informations
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like total numer of electrons, how many correlated atoms in the unit
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cell, and so on. It converts this hamiltonian into a hdf5 format and
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like total number of electrons, how many correlated atoms in the unit
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cell, and so on. It converts this Hamiltonian into a hdf5 format and
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sets some variables to standard values, such that it can be used with
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the python modules performing the DMFT calculation. How the
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hamiltonian matrix :math:`H_{mn}(\mathbf{k})` is actually calculated,
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is **not** part of this interace.
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Hamiltonian matrix :math:`H_{mn}(\mathbf{k})` is actually calculated,
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is **not** part of this interface.
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The DMFT calculation
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--------------------
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As mentioned above, there are a few python routines that allow to
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perform the multi-band DMFT calculation in the context of real
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materials. The major part is contained inte module
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materials. The major part is contained in the module
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:class:`SumkDFT`. It contains routines to
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* calculate local Greens functions
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@ -69,7 +72,7 @@ materials. The major part is contained inte module
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* calculate the double-counting correction
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* calculate the chemical potential in order to get the electron count right
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* other things like determining the structure of the local
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hamiltonian, rotating from local to global coordinate systems, etc.
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Hamiltonian, rotating from local to global coordinate systems, etc.
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At the user level, all these routines can be used to construct
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situation- and problem-dependent DMFT calculations in a very efficient
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@ -90,8 +93,8 @@ Post-processing
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The main result of DMFT calculation is the interacting Greens function
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and the Self energy. However, one is normally interested in
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quantitites like band structure, density of states, or transport
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properties. In order to calculate these things, :program:`dft_tools`
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quantities like band structure, density of states, or transport
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properties. In order to calculate these things, :program:`DFTTools`
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provides the post-processing modules :class:`SumkDFTTools`. It
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contains routines to calculate
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@ -102,11 +105,8 @@ contains routines to calculate
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or thermopower.
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.. warning::
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At the moment neither :ref:`TRIQS<triqslibs:welcome>` nor :program:`dft_tools`
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At the moment neither :ref:`TRIQS<triqslibs:welcome>` nor :program:`DFTTools`
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provides Maximum Entropy routines! You can use the Pade
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approximants implemented in the TRIQS library, or you use your own
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approximation implemented in the :ref:`TRIQS <triqslibs:welcome>` library, or you use your own
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home-made Maximum Entropy code to do the analytic continuation from
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Matsubara to the real-frequency axis.
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@ -17,7 +17,7 @@ extensions = ['sphinx.ext.autodoc',
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source_suffix = '.rst'
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project = u'TRIQS_DFT Tools'
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project = u'TRIQS DFTTools'
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copyright = u'2011-2013, M. Aichhorn, L. Pourovskii, V. Vildosola, C. Martins'
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version = '@DFT_TOOLS_VERSION@'
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release = '@DFT_TOOLS_RELEASE@'
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@ -28,16 +28,15 @@ templates_path = ['@CMAKE_SOURCE_DIR@/doc/_templates']
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html_theme = 'triqs'
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html_theme_path = ['@TRIQS_THEMES_PATH@']
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html_show_sphinx = False
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html_context = {'header_title': 'dft_tools',
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html_context = {'header_title': 'dft tools',
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'header_subtitle': 'connecting <a class="triqs" style="font-size: 12px" href="http://ipht.cea.fr/triqs">TRIQS</a> to DFT packages',
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'header_links': [['Install', 'install'],
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['Documentation', 'documentation'],
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['Issues', 'issues'],
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['About dft_tools', 'about']]}
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['About DFTTools', 'about']]}
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html_static_path = ['@CMAKE_SOURCE_DIR@/doc/_static']
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html_sidebars = {'index': ['sideb.html', 'searchbox.html']}
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htmlhelp_basename = 'TRIQSDftToolsdoc'
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intersphinx_mapping = {'python': ('http://docs.python.org/2.7', None), 'triqslibs': ('http://ipht.cea.fr/triqs', None),
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'triqscthyb': ('http://ipht.cea.fr/triqs/applications/cthyb', None)}
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intersphinx_mapping = {'python': ('http://docs.python.org/2.7', None), 'triqslibs': ('http://ipht.cea.fr/triqs', None), 'triqscthyb': ('http://ipht.cea.fr/triqs/applications/cthyb', None)}
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@ -1,4 +1,4 @@
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.. module:: pytriqs.applications.dft_tools
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.. module:: pytriqs.applications.dft
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.. _documentation:
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@ -11,6 +11,7 @@ Basic notions
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.. toctree::
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:maxdepth: 2
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basicnotions/first
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basicnotions/dft_dmft
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basicnotions/structure
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@ -23,6 +24,7 @@ User guide
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guide/conversion
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guide/dftdmft_singleshot
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guide/SrVO3
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guide/dftdmft_selfcons
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guide/analysis
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guide/full_tutorial
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@ -55,20 +55,21 @@ And next, we can initialize the :class:`SumkDFT <dft.sumk_dft.SumkDFT>` class::
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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. The
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minimal parameters for a SrVO3 DMFT calculation on 16 cores are::
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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"] = 50000
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p["n_cycles"] = 500000
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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"] = 60
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p["fit_max_n"] = 140
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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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@ -180,17 +181,26 @@ 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 is possible to build in convergence criterias.
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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 analyze 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 paramters
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------------------
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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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@ -7,13 +7,13 @@ This section explains how to use some tools of the package in order to analyse t
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There are two practical tools for which a self energy on the real axis is not needed, namely:
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* :meth:`dos_wannier_basis <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools.dos_wannier_basis>` for the density of states of the Wannier orbitals and
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* :meth:`partial_charges <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools.partial_charges>` for the partial charges according to the :program:`Wien2k` definition.
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* :meth:`dos_wannier_basis <dft.sumk_dft_tools.SumkDFTTools.dos_wannier_basis>` for the density of states of the Wannier orbitals and
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* :meth:`partial_charges <dft.sumk_dft_tools.SumkDFTTools.partial_charges>` for the partial charges according to the :program:`Wien2k` definition.
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However, a real frequency self energy has to be provided by the user for the methods:
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* :meth:`dos_parproj_basis <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools.dos_parproj_basis>` for the momentum-integrated spectral function including self energy effects and
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* :meth:`spaghettis <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools.spaghettis>` for the momentum-resolved spectral function (i.e. ARPES)
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* :meth:`dos_parproj_basis <dft.sumk_dft_tools.SumkDFTTools.dos_parproj_basis>` for the momentum-integrated spectral function including self energy effects and
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* :meth:`spaghettis <dft.sumk_dft_tools.SumkDFTTools.spaghettis>` for the momentum-resolved spectral function (i.e. ARPES)
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.. warning::
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This package does NOT provide an explicit method to do an **analytic continuation** of the
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@ -24,26 +24,26 @@ However, a real frequency self energy has to be provided by the user for the met
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Initialisation
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--------------
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All tools described below are collected in an extension of the :class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>` class and are
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loaded by importing the module :class:`SumkDFTTools <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools>`::
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All tools described below are collected in an extension of the :class:`SumkDFT <dft.sumk_dft.SumkDFT>` class and are
|
||||
loaded by importing the module :class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>`::
|
||||
|
||||
from pytriqs.applications.dft.sumk_dft_tools import *
|
||||
|
||||
The initialisation of the class is equivalent to that of the :class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>`
|
||||
The initialisation of the class is equivalent to that of the :class:`SumkDFT <dft.sumk_dft.SumkDFT>`
|
||||
class::
|
||||
|
||||
SK = SumkDFTTools(hdf_file = filename + '.h5')
|
||||
|
||||
Note that all routines available in :class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>` are also available here.
|
||||
Note that all routines available in :class:`SumkDFT <dft.sumk_dft.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 <pytriqs.gf.local.BlockGf>` object
|
||||
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 <pytriqs.gf.local.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 the :ref:`TRIQS <triqslibs:welcome>` library offers
|
||||
You may also have your self energy stored in text files. For this case the :ref:`TRIQS <triqslibs:welcome>` library offers
|
||||
the function :meth:`read_gf_from_txt`, which is able to load the data from text files of one Greens function block
|
||||
into a real frequency :class:`ReFreqGf <pytriqs.gf.local.ReFreqGf>` object. Loading each block separately and
|
||||
building up a :class:´BlockGf <pytriqs.gf.local.BlockGf>´ is done with::
|
||||
@ -58,18 +58,18 @@ building up a :class:´BlockGf <pytriqs.gf.local.BlockGf>´ is done with::
|
||||
|
||||
where:
|
||||
|
||||
* `block_txtfiles` is a rank 2 square np.array(str) or list[list[str]] holding the file names of one block and
|
||||
* `block_txtfiles` is a rank 2 square np.array(str) or list[list[str]] holding the file names of one block and
|
||||
* `block_name` is the name of the block.
|
||||
|
||||
It is important that each data file has to contain three columns: the real frequency mesh, the real part and the imaginary part
|
||||
of the self energy - exactly in this order! The mesh should be the same for all files read in and non-uniform meshes are not supported.
|
||||
|
||||
Finally, we set the self energy into the `SK` object::
|
||||
|
||||
of the self energy - exactly in this order! The mesh should be the same for all files read in and non-uniform meshes are not supported.
|
||||
|
||||
Finally, we set the self energy into the `SK` object::
|
||||
|
||||
SK.set_Sigma([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)
|
||||
@ -84,16 +84,16 @@ 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
|
||||
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
|
||||
* `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
|
||||
* `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 output is returned by the function for a further usage in :program:`python`.
|
||||
@ -110,7 +110,7 @@ real frequency self energy for this purpose. The calculation is done by::
|
||||
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 <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools.partial_charges>`.
|
||||
in the hdf5 archive. For the structure of `dm`, see also :meth:`reference manual <dft.sumk_dft_tools.SumkDFTTools.partial_charges>`.
|
||||
|
||||
Correlated spectral function (with real frequency self energy)
|
||||
--------------------------------------------------------------
|
||||
@ -129,7 +129,7 @@ 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 <pytriqs.applications.dft.converters.wien2k_converter.Wien2kConverter.convert_bands_input>`
|
||||
option and use the :meth:`convert_bands_input <dft.converters.wien2k_converter.Wien2kConverter.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_')
|
||||
|
||||
@ -34,9 +34,9 @@ some files that we need for the Wannier orbital construction.
|
||||
The orbital construction itself is done by the Fortran program
|
||||
:program:`dmftproj`. For an extensive manual to this program see
|
||||
:download:`TutorialDmftproj.pdf <images_scripts/TutorialDmftproj.pdf>`.
|
||||
Here we will only describe only the basic steps.
|
||||
Here we will only describe the basic steps.
|
||||
|
||||
Let us take the example of SrVO3, a commonly used
|
||||
Let us take the compound SrVO3, a commonly used
|
||||
example for DFT+DMFT calculations. The input file for
|
||||
:program:`dmftproj` looks like
|
||||
|
||||
@ -56,9 +56,9 @@ following 3 to 5 lines:
|
||||
harmonics).
|
||||
#. The four numbers refer to *s*, *p*, *d*, and *f* electrons,
|
||||
resp. Putting 0 means doing nothing, putting 1 will calculate
|
||||
**unnormalised** projectors in compliance with the Wien2k
|
||||
**unnormalized** projectors in compliance with the Wien2k
|
||||
definition. The important flag is 2, this means to include these
|
||||
electrons as correlated electrons, and calculate normalised Wannier
|
||||
electrons as correlated electrons, and calculate normalized Wannier
|
||||
functions for them. In the example above, you see that only for the
|
||||
vanadium *d* we set the flag to 2. If you want to do simply a DMFT
|
||||
calculation, then set everything to 0, except one flag 2 for the
|
||||
@ -100,12 +100,12 @@ directory name):
|
||||
respectively. These files are needed for projected
|
||||
density-of-states or spectral-function calculations in
|
||||
post-processing only.
|
||||
* :file:`case.oubwin` needed for the charge desity recalculation in
|
||||
* :file:`case.oubwin` needed for the charge density recalculation in
|
||||
the case of fully self-consistent DFT+DMFT run (see below).
|
||||
|
||||
Now we convert these files into an hdf5 file that can be used for the
|
||||
DMFT calculations. For this purpose we
|
||||
use the python module :class:`Wien2kConverter <pytriqs.applications.dft.converters.wien2k_converter.Wien2kConverter>`. It is initialised as::
|
||||
use the python module :class:`Wien2kConverter <dft.converters.wien2k_converter.Wien2kConverter>`. It is initialized as::
|
||||
|
||||
from pytriqs.applications.dft.converters.wien2k_converter import *
|
||||
Converter = Wien2kConverter(filename = case)
|
||||
@ -119,7 +119,7 @@ an hdf5 archive, named :file:`case.h5`, where all the data is
|
||||
stored. For other parameters of the constructor please visit the
|
||||
:ref:`refconverters` section of the reference manual.
|
||||
|
||||
After initialising the interface module, we can now convert the input
|
||||
After initializing the interface module, we can now convert the input
|
||||
text files to the hdf5 archive by::
|
||||
|
||||
Converter.convert_dft_input()
|
||||
@ -133,21 +133,21 @@ After this step, all the necessary information for the DMFT loop is
|
||||
stored in the hdf5 archive, where the string variable
|
||||
`Converter.hdf_filename` gives the file name of the archive.
|
||||
|
||||
At this point you should use the method :meth:`dos_wannier_basis <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools.dos_wannier_basis>`
|
||||
contained in the module :class:`SumkDFTTools <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools>` to check the density of
|
||||
states of the Wannier orbitals (see :ref:`analysis`).
|
||||
At this point you should use the method :meth:`dos_wannier_basis <dft.sumk_dft_tools.SumkDFTTools.dos_wannier_basis>`
|
||||
contained in the module :class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>` to check the density of
|
||||
states of the Wannier orbitals (see :ref:`analysis`).
|
||||
|
||||
You have now everything for performing a DMFT calculation, and you can
|
||||
proceed with :ref:`singleshot`.
|
||||
proceed with the section on :ref:`single-shot DFT+DMFT calculations <singleshot>`.
|
||||
|
||||
Data for post-processing
|
||||
""""""""""""""""""""""""
|
||||
|
||||
In case you want to do post-processing of your data using the module
|
||||
:class:`SumkDFTTools <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools>`, some more files
|
||||
:class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>`, some more files
|
||||
have to be converted to the hdf5 archive. For instance, for
|
||||
calculating the partial density of states or partial charges
|
||||
consistent with the definition of :program:`Wien2k`, you have to invoke::
|
||||
consistent with the definition of :program:`Wien2k`, you have to invoke::
|
||||
|
||||
Converter.convert_parproj_input()
|
||||
|
||||
@ -165,8 +165,8 @@ following. First, one has to do the Wien2k calculation on the given
|
||||
|
||||
Again, maybe with the optional additional extra flags according to
|
||||
Wien2k. Now we use a routine of the converter module allows to read
|
||||
and convert the input for :class:`SumkDFTTools <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools>`::
|
||||
|
||||
and convert the input for :class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>`::
|
||||
|
||||
Converter.convert_bands_input()
|
||||
|
||||
After having converted this input, you can further proceed with the
|
||||
@ -186,7 +186,7 @@ A general H(k)
|
||||
--------------
|
||||
|
||||
In addition to the more complicated Wien2k converter,
|
||||
:program:`dft_tools` contains also a light converter. It takes only
|
||||
:program:`DFTTools` contains also a light converter. It takes only
|
||||
one inputfile, and creates the necessary hdf outputfile for
|
||||
the DMFT calculation. The header of this input file has to have the
|
||||
following format:
|
||||
@ -204,15 +204,13 @@ The lines of this header define
|
||||
#. The last line contains several numbers: the number of irreducible
|
||||
representations, and then the dimensions of the irreps. One
|
||||
possibility is as the example above, another one would be 2
|
||||
2 3. Thiw would mean, 2 irreps (eg and t2g), of dimension 2 and 3,
|
||||
resp.
|
||||
2 3. This would mean, 2 irreps (eg and t2g), of dimension 2 and 3,
|
||||
resp.
|
||||
|
||||
After these header lines, the file has to contain the Hamiltonian
|
||||
matrix in orbital space. The standard convention is that you give for
|
||||
each
|
||||
:math:`\mathbf{k}`-point first the matrix of the real part, then the
|
||||
matrix of the imaginary part, and then move on to the next
|
||||
:math:`\mathbf{k}`-point.
|
||||
each :math:`\mathbf{k}`-point first the matrix of the real part, then the
|
||||
matrix of the imaginary part, and then move on to the next :math:`\mathbf{k}`-point.
|
||||
|
||||
The converter itself is used as::
|
||||
|
||||
@ -221,8 +219,7 @@ The converter itself is used as::
|
||||
Converter.convert_dft_input()
|
||||
|
||||
where :file:`hkinputfile` is the name of the input file described
|
||||
above. This produces the hdf file that you need, and you cna proceed
|
||||
with the
|
||||
above. This produces the hdf file that you need for a DMFT calculation.
|
||||
|
||||
For more options of this converter, have a look at the
|
||||
:ref:`refconverters` section of the reference manual.
|
||||
@ -231,24 +228,24 @@ For more options of this converter, have a look at the
|
||||
Wannier90 Converter
|
||||
-------------------
|
||||
|
||||
Using this converter it is possible to convert the output of
|
||||
:program:`Wannier90` (http://wannier.org) calculations of
|
||||
Maximally Localized Wannier Functions (MLWF) and create a HDF5 archive
|
||||
Using this converter it is possible to convert the output of
|
||||
`wannier90 <http://wannier.org>`_
|
||||
Maximally Localized Wannier Functions (MLWF) and create a HDF5 archive
|
||||
suitable for one-shot DMFT calculations with the
|
||||
:class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>` class.
|
||||
:class:`SumkDFT <dft.sumk_dft.SumkDFT>` class.
|
||||
|
||||
The user must supply two files in order to run the Wannier90 Converter:
|
||||
|
||||
#. The file :file:`seedname_hr.dat`, which contains the DFT Hamiltonian
|
||||
in the MLWF basis calculated through :program:`wannier90` with ``hr_plot = true``
|
||||
(please refer to the :program:`wannier90` documentation).
|
||||
#. A file named :file:`seedname.inp`, which contains the required
|
||||
#. A file named :file:`seedname.inp`, which contains the required
|
||||
information about the :math:`\mathbf{k}`-point mesh, the electron density,
|
||||
the correlated shell structure, ... (see below).
|
||||
|
||||
Here and in the following, the keyword ``seedname`` should always be intended
|
||||
as a placeholder for the actual prefix chosen by the user when creating the
|
||||
input for :program:`wannier90`.
|
||||
input for :program:`wannier90`.
|
||||
Once these two files are available, one can use the converter as follows::
|
||||
|
||||
from pytriqs.applications.dft.converters import Wannier90Converter
|
||||
@ -260,8 +257,8 @@ the following format:
|
||||
|
||||
.. literalinclude:: images_scripts/LaVO3_w90.inp
|
||||
|
||||
The example shows the input for the perovskite crystal of LaVO\ :sub:`3`
|
||||
in the room-temperature `Pnma` symmetry. The unit cell contains four
|
||||
The example shows the input for the perovskite crystal of LaVO\ :sub:`3`
|
||||
in the room-temperature `Pnma` symmetry. The unit cell contains four
|
||||
symmetry-equivalent correlated sites (the V atoms) and the total number
|
||||
of electrons per unit cell is 8 (see second line).
|
||||
The first line specifies how to generate the :math:`\mathbf{k}`-point
|
||||
@ -269,18 +266,18 @@ mesh that will be used to obtain :math:`H(\mathbf{k})`
|
||||
by Fourier transforming :math:`H(\mathbf{R})`.
|
||||
Currently implemented options are:
|
||||
|
||||
* :math:`\Gamma`-centered uniform grid with dimensions
|
||||
:math:`n_{k_x} \times n_{k_y} \times n_{k_z}`;
|
||||
* :math:`\Gamma`-centered uniform grid with dimensions
|
||||
:math:`n_{k_x} \times n_{k_y} \times n_{k_z}`;
|
||||
specify ``0`` followed by the three grid dimensions,
|
||||
like in the example above
|
||||
* :math:`\Gamma`-centered uniform grid with dimensions
|
||||
automatically determined by the converter (from the number of
|
||||
automatically determined by the converter (from the number of
|
||||
:math:`\mathbf{R}` vectors found in :file:`seedname_hr.dat`);
|
||||
just specify ``-1``
|
||||
|
||||
Inside :file:`seedname.inp`, it is crucial to correctly specify the
|
||||
Inside :file:`seedname.inp`, it is crucial to correctly specify the
|
||||
correlated shell structure, which depends on the contents of the
|
||||
:program:`wannier90` output :file:`seedname_hr.dat` and on the order
|
||||
:program:`wannier90` output :file:`seedname_hr.dat` and on the order
|
||||
of the MLWFs contained in it.
|
||||
|
||||
The number of MLWFs must be equal to, or greater than the total number
|
||||
@ -291,7 +288,7 @@ additional MLWFs correspond to uncorrelated orbitals (e.g., the O-\ `2p` shells)
|
||||
When reading the hoppings :math:`\langle w_i | H(\mathbf{R}) | w_j \rangle`
|
||||
(where :math:`w_i` is the :math:`i`-th MLWF), the converter also assumes that
|
||||
the first indices correspond to the correlated shells (in our example,
|
||||
the V-t\ :sub:`2g` shells). Therefore, the MLWFs corresponding to the
|
||||
the V-t\ :sub:`2g` shells). Therefore, the MLWFs corresponding to the
|
||||
uncorrelated shells (if present) must be listed **after** those of the
|
||||
correlated shells.
|
||||
With the :program:`wannier90` code, this can be achieved this by listing the
|
||||
@ -303,19 +300,19 @@ In our `Pnma`-LaVO\ :sub:`3` example, for instance, we could use::
|
||||
O:l=1:mr=1,2,3:z=0,0,1:x=-1,1,0
|
||||
End Projections
|
||||
|
||||
where the ``x=-1,1,0`` option indicates that the V--O bonds in the octahedra are
|
||||
where the ``x=-1,1,0`` option indicates that the V--O bonds in the octahedra are
|
||||
rotated by (approximatively) 45 degrees with respect to the axes of the `Pbnm` cell.
|
||||
|
||||
The converter will analyse the matrix elements of the local hamiltonian
|
||||
to find the symmetry matrices `rot_mat` needed for the global-to-local
|
||||
transformation of the basis set for correlated orbitals
|
||||
The converter will analyze the matrix elements of the local Hamiltonian
|
||||
to find the symmetry matrices `rot_mat` needed for the global-to-local
|
||||
transformation of the basis set for correlated orbitals
|
||||
(see section :ref:`hdfstructure`).
|
||||
The matrices are obtained by finding the unitary transformations that diagonalize
|
||||
:math:`\langle w_i | H_I(\mathbf{R}=0,0,0) | w_j \rangle`, where :math:`I` runs
|
||||
over the correlated shells and `i,j` belong to the same shell (more details elsewhere...).
|
||||
If two correlated shells are defined as equivalent in :file:`seedname.inp`,
|
||||
then the corresponding eigenvalues have to match within a threshold of 10\ :sup:`-5`,
|
||||
otherwise the converter will produce an error/warning.
|
||||
otherwise the converter will produce an error/warning.
|
||||
If this happens, please carefully check your data in :file:`seedname_hr.dat`.
|
||||
This method might fail in non-trivial cases (i.e., more than one correlated
|
||||
shell is present) when there are some degenerate eigenvalues:
|
||||
@ -330,10 +327,10 @@ The current implementation of the Wannier90 Converter has some limitations:
|
||||
* No charge self-consistency possible at the moment.
|
||||
* Calculations with spin-orbit (``SO=1``) are not supported.
|
||||
* The spin-polarized case (``SP=1``) is not yet tested.
|
||||
* The post-processing routines in the module
|
||||
:class:`SumkDFTTools <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools>`
|
||||
were not tested with this converter.
|
||||
* ``proj_mat_all`` are not used, so there are no projectors onto the
|
||||
* The post-processing routines in the module
|
||||
:class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>`
|
||||
were not tested with this converter.
|
||||
* ``proj_mat_all`` are not used, so there are no projectors onto the
|
||||
uncorrelated orbitals for now.
|
||||
|
||||
|
||||
@ -344,14 +341,14 @@ The interface packages are written such that all the file operations
|
||||
are done only on the master node. In general, the philosophy of the
|
||||
package is that whenever you read in something from the archive
|
||||
yourself, you have to *manually* broadcast it to the nodes. An
|
||||
exception to this rule is when you use routines from :class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>`
|
||||
or :class:`SumkDFTTools <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools>`, where the broadcasting is done for you.
|
||||
exception to this rule is when you use routines from :class:`SumkDFT <dft.sumk_dft.SumkDFT>`
|
||||
or :class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>`, where the broadcasting is done for you.
|
||||
|
||||
Interfaces to other packages
|
||||
----------------------------
|
||||
|
||||
Because of the modular structure, it is straight forward to extend the :ref:`TRIQS <triqslibs:welcome>` package
|
||||
in order to work with other band-structure codes. The only necessary requirement is that
|
||||
Because of the modular structure, it is straight forward to extend the :ref:`TRIQS <triqslibs:welcome>` package
|
||||
in order to work with other band-structure codes. The only necessary requirement is that
|
||||
the interface module produces an hdf5 archive, that stores all the data in the specified
|
||||
form. For the details of what data is stored in detail, see the
|
||||
:ref:`hdfstructure` part of the reference manual.
|
||||
|
||||
@ -5,287 +5,163 @@
|
||||
Single-shot DFT+DMFT
|
||||
====================
|
||||
|
||||
After having set up the hdf5 archive, we can now proceed to our first DFT+DMFT calculation.
|
||||
It consists of initialization steps, and the actual DMFT self-consistency loop,
|
||||
With the code snippets below you can build your own script and target
|
||||
it to your needs. Little examples on :ref:`mixing <mixing>` and on
|
||||
:ref:`restarting from a previous calculation <restartcalc>` at the end of this page
|
||||
should also demonstrate how simple you can modify your own DMFT script. A full working
|
||||
calculation for SrVO3 is discussed in the :ref:`next section <SrVO3>`.
|
||||
|
||||
After having set up the hdf5 archive, we can now do our DFT+DMFT calculation. It consists of
|
||||
initialization steps, and the actual DMFT self-consistency loop, as is
|
||||
discussed below.
|
||||
|
||||
Initialisation of the calculation
|
||||
Initialization of the calculation
|
||||
---------------------------------
|
||||
|
||||
Before doing the calculation, we have to intialize all the objects that we will need. The first thing is the
|
||||
:class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>` class. It contains all basic routines that are necessary to perform a summation in k-space
|
||||
Before doing the actual calculation, we have to initialize all needed objects.
|
||||
The first thing is the :class:`SumkDFT <dft.sumk_dft.SumkDFT>` class.
|
||||
It contains all basic routines that are necessary to perform a summation in k-space
|
||||
to get the local quantities used in DMFT. It is initialized by::
|
||||
|
||||
from pytriqs.applications.dft.sumk_dft import *
|
||||
SK = SumkDFT(hdf_file = filename + '.h5')
|
||||
from pytriqs.applications.dft.sumk_dft import *
|
||||
SK = SumkDFT(hdf_file = filename + '.h5')
|
||||
|
||||
|
||||
Setting up the impurity solver
|
||||
------------------------------
|
||||
|
||||
The next step is to setup an impurity solver. There are different
|
||||
solvers available within the :ref:`TRIQS <triqslibs:welcome>` framework. Below, we will discuss
|
||||
the example of the hybridisation
|
||||
solvers available within the :ref:`TRIQS <triqslibs:welcome>` framework.
|
||||
E.g. for :ref:`SrVO3 <SrVO3>`, we will use the hybridization
|
||||
expansion :ref:`CTHYB solver <triqscthyb:welcome>`. Later on, we will
|
||||
see also the example of the Hubbard-I solver. They all have in common,
|
||||
that they are called by a uniform command::
|
||||
|
||||
S.solve(params)
|
||||
see also the example of the `Hubbard-I solver <http://ipht.cea.fr/triqs/applications/hubbardI>`_.
|
||||
They all have in common, that they are called by an uniform command::
|
||||
|
||||
where `params` are the solver parameters and depend on the actual
|
||||
solver that is used. Before going into the details of the solver, let
|
||||
us discuss in the next section how to perform the DMFT loop using
|
||||
the methods of :program:`dft_tools`, assuming that we have set up a
|
||||
working solver instance.
|
||||
S.solve(params)
|
||||
|
||||
where :emphasis:`params` are the solver parameters and depend on the actual
|
||||
solver. Setting up the :ref:`CTHYB solver <triqscthyb:welcome>` for SrVO3 is
|
||||
discussed on the :ref:`next page <SrVO3>`. Here, let us now perform the DMFT
|
||||
loop using the methods of :program:`DFTTools`, assuming that we have already
|
||||
set up a working solver instance.
|
||||
|
||||
|
||||
Doing the DMFT loop
|
||||
-------------------
|
||||
|
||||
Having initialized the SumK class and the Solver, we can proceed with the DMFT
|
||||
loop itself. We have to set up the loop over DMFT
|
||||
iterations and the self-consistency condition::
|
||||
Having initialized the :class:`Sumk class <dft.sumk_dft.SumkDFT>`
|
||||
and the solver, we can proceed with the actual DMFT part of the calculation.
|
||||
We set up the loop over DMFT iterations and the self-consistency condition::
|
||||
|
||||
n_loops = 5
|
||||
for iteration_number in range(n_loops) : # start the DMFT loop
|
||||
n_loops = 15
|
||||
for iteration_number in range(n_loops) : # start the DMFT loop
|
||||
SK.set_Sigma([ S.Sigma ]) # Put self energy to the SumK class
|
||||
chemical_potential = SK.calc_mu() # calculate the chemical potential for the given density
|
||||
S.G_iw << SK.extract_G_loc()[0] # extract the local Green function
|
||||
S.G0_iw << inverse(S.Sigma_iw + inverse(S.G_iw)) # finally get G0, the input for the solver
|
||||
|
||||
SK.set_Sigma([ S.Sigma ]) # Put self energy to the SumK class
|
||||
chemical_potential = SK.calc_mu() # calculate the chemical potential for the given density
|
||||
S.G_iw << SK.extract_G_loc()[0] # extract the local Green function
|
||||
S.G0_iw << inverse(S.Sigma_iw + inverse(S.G_iw)) # finally get G0, the input for the Solver
|
||||
S.solve(h_int=h_int, **p) # now solve the impurity problem
|
||||
|
||||
S.solve(h_int=h_int, **p) # now solve the impurity problem
|
||||
dm = S.G_iw.density() # Density matrix of the impurity problem
|
||||
SK.calc_dc(dm, U_interact=U, J_hund=J, orb=0, use_dc_formula=1) # Set the double counting term
|
||||
SK.save(['chemical_potential','dc_imp','dc_energ']) # Save data in the hdf5 archive
|
||||
|
||||
dm = S.G_iw.density() # Density matrix of the impurity problem
|
||||
SK.calc_dc(dm, U_interact=U, J_hund=J, orb=0, use_dc_formula=1) # Set the double counting term
|
||||
SK.save(['chemical_potential','dc_imp','dc_energ']) # Save data in the hdf5 archive
|
||||
|
||||
These basic steps are enough to set up the basic DMFT Loop. For a detailed
|
||||
description of the :class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>` routines, see the reference
|
||||
manual.
|
||||
|
||||
After
|
||||
the self-consistency steps (extracting a new :math:`G^0(i\omega)`),
|
||||
the Anderson impurity problem is solved.
|
||||
|
||||
Different to model calculations, we have to do a few
|
||||
These steps are enough for a basic DMFT Loop.
|
||||
After the self-consistency steps, which lead to a new :math:`G^0(i\omega)`,
|
||||
the impurity solver is called. Different to model calculations, we have to do a few
|
||||
more steps after this, because of the double-counting correction. We first
|
||||
calculate the density of the impurity problem. Then, the routine `calc_dc`
|
||||
calculate the density of the impurity problem. Then, the routine :meth:`calc_dc <dft.sumk_dft.SumkDFT.calc_dc>`
|
||||
takes as parameters this density matrix, the Coulomb interaction, Hund's rule
|
||||
coupling, and the type of double-counting that should be used. Possible values
|
||||
for `use_dc_formula` are:
|
||||
for :emphasis:`use_dc_formula` are:
|
||||
|
||||
* `0`: Full-localised limit
|
||||
* `1`: DC formula as given in K. Held, Adv. Phys. 56, 829 (2007).
|
||||
* `2`: Around-mean-field
|
||||
* `0`: Full-localised limit (FLL)
|
||||
* `1`: DC formula as given in K. Held, Adv. Phys. 56, 829 (2007).
|
||||
* `2`: Around-mean-field (AMF)
|
||||
|
||||
At the end of the calculation, we can save the Greens function and self energy into a file::
|
||||
|
||||
from pytriqs.archive import HDFArchive
|
||||
import pytriqs.utility.mpi as mpi
|
||||
if mpi.is_master_node():
|
||||
ar = HDFArchive("YourDFTDMFTcalculation.h5",'w')
|
||||
ar["G"] = S.G_iw
|
||||
ar["Sigma"] = S.Sigma_iw
|
||||
|
||||
This is it!
|
||||
|
||||
These are the essential steps to do a one-shot DFT+DMFT calculation.
|
||||
For full charge-self consistent calculations, there are some more things
|
||||
to consider, which we will see later on.
|
||||
|
||||
|
||||
A full DFT+DMFT calculation
|
||||
---------------------------
|
||||
|
||||
We will discuss now how to set up a full working calculation,
|
||||
including setting up the CTHYB solver, and specifying some more parameters
|
||||
in order to make the calculation more efficient. Here, we
|
||||
will see a more advanced example, which is also suited for parallel
|
||||
execution. 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.
|
||||
|
||||
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 CTHYB
|
||||
solver.
|
||||
|
||||
Then we define some parameters::
|
||||
|
||||
dft_filename='SrVO3'
|
||||
U = 4.0
|
||||
J = 0.65
|
||||
beta = 40
|
||||
loops = 10 # Number of DMFT sc-loops
|
||||
sigma_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
|
||||
|
||||
# Solver parameters
|
||||
p = {}
|
||||
p["length_cycle"] = 200
|
||||
p["n_warmup_cycles"] = 2000
|
||||
p["n_cycles"] = 20000
|
||||
|
||||
Most of these parameters are self-explanatory. The first,
|
||||
`dft_filename`, gives the filename of the input files. For more
|
||||
details on the solver parameters, we refer the user to
|
||||
the :ref:`CTHYB solver <triqscthyb:welcome>` documentation.
|
||||
|
||||
We assume that the conversion to the hdf5 archive is already done. We
|
||||
can check now in this archive, if previous runs are present, or if we have to start
|
||||
from scratch::
|
||||
|
||||
previous_runs = 0
|
||||
previous_present = False
|
||||
if mpi.is_master_node():
|
||||
f = HDFArchive(dft_filename+'.h5','a')
|
||||
if 'dmft_output' in f:
|
||||
ar = f['dmft_output']
|
||||
if 'iterations' in ar:
|
||||
previous_present = True
|
||||
previous_runs = ar['iterations']
|
||||
else:
|
||||
f.create_group('dmft_output')
|
||||
del f
|
||||
previous_runs = mpi.bcast(previous_runs)
|
||||
previous_present = mpi.bcast(previous_present)
|
||||
|
||||
|
||||
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`. Removing this subgroup allows you to reset your
|
||||
calculation to the starting point easily.
|
||||
|
||||
Now we can use all this information to initialise the :class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>` class::
|
||||
|
||||
SK = SumkDFT(hdf_file=dft_filename+'.h5',use_dft_blocks=use_blocks)
|
||||
|
||||
The next step is to initialise the :class:`Solver <pytriqs.applications.impurity_solvers.cthyb.Solver>` class. It consist
|
||||
of two steps
|
||||
|
||||
#. Calculating the multi-band interaction matrix, and setting up the
|
||||
interaction Hamiltonian
|
||||
#. Setting up the solver class
|
||||
|
||||
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`. For
|
||||
other choices (Slater interaction matrix for instance), and other
|
||||
parameters, we refer to the reference manual
|
||||
of the :ref:`TRIQS <triqslibs:welcome>` library.
|
||||
|
||||
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 choices for the Hamiltonian are
|
||||
|
||||
* h_int_kanamori
|
||||
* h_int_slater
|
||||
|
||||
These two include full rotational invariant interactions. Again,
|
||||
options can be found in the :ref:`TRIQS <triqslibs:welcome>` library
|
||||
reference manual.
|
||||
|
||||
|
||||
If there are previous runs stored in the hdf5 archive, we can now load the self energy
|
||||
of the last iteration::
|
||||
|
||||
if previous_present:
|
||||
from pytriqs.archive import HDFArchive
|
||||
import pytriqs.utility.mpi as mpi
|
||||
if mpi.is_master_node():
|
||||
ar = HDFArchive(dft_filename+'.h5','a')
|
||||
S.Sigma_iw << ar['dmft_output']['Sigma_iw']
|
||||
del ar
|
||||
ar = HDFArchive("YourDFTDMFTcalculation.h5",'w')
|
||||
ar["G"] = S.G_iw
|
||||
ar["Sigma"] = S.Sigma_iw
|
||||
|
||||
These are the essential steps necessary for a one-shot DFT+DMFT calculation.
|
||||
For a detailed description of the :class:`SumkDFT <dft.sumk_dft.SumkDFT>`
|
||||
routines, see the :ref:`reference manual <reference>`. To perform full charge self-consistent calculations, there
|
||||
are some more things to consider, which we will see :ref:`later on <full_charge_selfcons>`.
|
||||
|
||||
.. _restartcalc:
|
||||
|
||||
|
||||
Restarting a calculation
|
||||
------------------------
|
||||
|
||||
Often only a few DMFT iterations are performed first, and thus, it is desirable to
|
||||
carry out further iterations, e.g. to improve on the convergence. With a little modification
|
||||
at the initialization stage (before the DMFT loop) it is possible to detect if previous runs
|
||||
are present, or if the calculation should start from scratch::
|
||||
|
||||
previous_runs = 0
|
||||
previous_present = False
|
||||
if mpi.is_master_node():
|
||||
f = HDFArchive(dft_filename+'.h5','a')
|
||||
if 'dmft_output' in f:
|
||||
ar = f['dmft_output']
|
||||
if 'iterations' in ar:
|
||||
previous_present = True
|
||||
previous_runs = ar['iterations']
|
||||
else:
|
||||
f.create_group('dmft_output')
|
||||
del f
|
||||
previous_runs = mpi.bcast(previous_runs)
|
||||
previous_present = mpi.bcast(previous_present)
|
||||
|
||||
|
||||
You can see from this code snippet, that removing the subgroup :emphasis:`dmft_results` from the
|
||||
hdf file has the effect of reseting the calculation to the starting point. If there are previous
|
||||
runs stored in the hdf5 archive, we can now load the self energy, the chemical potential and
|
||||
double counting values of the last iteration::
|
||||
|
||||
if previous_present:
|
||||
if mpi.is_master_node():
|
||||
ar = HDFArchive(dft_filename+'.h5','a')
|
||||
S.Sigma_iw << ar['dmft_output']['Sigma_iw']
|
||||
del ar
|
||||
|
||||
S.Sigma_iw << mpi.bcast(S.Sigma_iw)
|
||||
chemical_potential,dc_imp,dc_energ = SK.load(['chemical_potential','dc_imp','dc_energ'])
|
||||
S.Sigma_iw << mpi.bcast(S.Sigma_iw)
|
||||
SK.set_mu(chemical_potential)
|
||||
SK.set_dc(dc_imp,dc_energ)
|
||||
SK.set_mu(chemical_potential)
|
||||
SK.set_dc(dc_imp,dc_energ)
|
||||
|
||||
The data is loaded only on the master node, and therefore we broadcast it to the slave nodes.
|
||||
Be careful when storing the :emphasis:`iteration_number` as we also have to add the previous
|
||||
iteration count::
|
||||
|
||||
ar['dmft_output']['iterations'] = iteration_number + previous_runs
|
||||
|
||||
The self-energy is broadcast from the master node to the slave nodes. Also, the
|
||||
last saved chemical potential and double counting values are read in and set.
|
||||
.. _mixing:
|
||||
|
||||
Now we can go to the definition of the self-consistency step. It consists again
|
||||
of the basic steps discussed in the 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) # symmetrise 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)
|
||||
Mixing
|
||||
------
|
||||
|
||||
# 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 sigma_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"%sigma_mix)
|
||||
S.Sigma_iw << sigma_mix * S.Sigma_iw + (1.0-sigma_mix) * ar['dmft_output']['Sigma_iw']
|
||||
S.G_iw << sigma_mix * S.G_iw + (1.0-sigma_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 + previous_runs
|
||||
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
|
||||
In some cases a mixing of two consecutive self energies (or alternatively two hybridization
|
||||
functions) can be necessary in order to ensure convergence::
|
||||
|
||||
# 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)
|
||||
mix = 0.8 # mixing factor
|
||||
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)
|
||||
|
||||
# Save stuff into the dft_output 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. At the end, all results are stored in the hdf5 output file.
|
||||
In this little piece of code, which should be placed after calling the solver, two consecutive
|
||||
self energies are linearly mixed with the factor :emphasis:`mix`. Of course, it is possible
|
||||
to implement more advanced mixing schemes (e.g. Broyden's methods), however, in most cases
|
||||
simple linear mixing or even no mixing is sufficient for a reasonably fast convergence.
|
||||
|
||||
@ -89,7 +89,7 @@ however there are also some differences. First difference is that we import the
|
||||
|
||||
The Hubbard-I solver is very fast and we do not need to take into account the DFT block structure or use any approximation for the *U*-matrix.
|
||||
We load and convert the :program:`dmftproj` output and initialize the
|
||||
:class:`SumkDFT <pytriqs.applications.dft.sumk_dft.SumkDFT>` class as described in :ref:`conversion` and
|
||||
:class:`SumkDFT <dft.sumk_dft.SumkDFT>` class as described in :ref:`conversion` and
|
||||
:ref:`singleshot` and then set up the Hubbard-I solver ::
|
||||
|
||||
S = Solver(beta = beta, l = l)
|
||||
@ -206,7 +206,7 @@ symmetries::
|
||||
Converter.convert_parpoj_input()
|
||||
|
||||
To get access to analysing tools we initialize the
|
||||
:class:`SumkDFTTools <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools>` class ::
|
||||
:class:`SumkDFTTools <dft.sumk_dft_tools.SumkDFTTools>` class ::
|
||||
|
||||
SK = SumkDFTTools(hdf_file=dft_filename+'.h5', use_dft_blocks=False)
|
||||
|
||||
|
||||
BIN
doc/guide/images_scripts/SrVO3_Sigma_iw_it1.png
Normal file
BIN
doc/guide/images_scripts/SrVO3_Sigma_iw_it1.png
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 46 KiB |
@ -6,10 +6,10 @@ from pytriqs.gf.local import *
|
||||
from pytriqs.applications.dft.sumk_dft import *
|
||||
|
||||
dft_filename='SrVO3'
|
||||
U = U.0
|
||||
U = 4.0
|
||||
J = 0.65
|
||||
beta = 40
|
||||
loops = 10 # Number of DMFT sc-loops
|
||||
loops = 15 # Number of DMFT sc-loops
|
||||
sigma_mix = 1.0 # Mixing factor of Sigma after solution of the AIM
|
||||
delta_mix = 1.0 # Mixing factor of Delta as input for the AIM
|
||||
dc_type = 1 # DC type: 0 FLL, 1 Held, 2 AMF
|
||||
@ -20,9 +20,14 @@ h_field = 0.0
|
||||
# Solver parameters
|
||||
p = {}
|
||||
p["max_time"] = -1
|
||||
p["length_cycle"] = 50
|
||||
p["n_warmup_cycles"] = 50
|
||||
p["n_cycles"] = 5000
|
||||
p["random_seed"] = 123 * mpi.rank + 567
|
||||
p["length_cycle"] = 200
|
||||
p["n_warmup_cycles"] = 100000
|
||||
p["n_cycles"] = 1000000
|
||||
p["perfrom_tail_fit"] = True
|
||||
p["fit_max_moments"] = 4
|
||||
p["fit_min_n"] = 30
|
||||
p["fit_max_n"] = 60
|
||||
|
||||
# If conversion step was not done, we could do it here. Uncomment the lines it you want to do this.
|
||||
#from pytriqs.applications.dft.converters.wien2k_converter import *
|
||||
@ -141,6 +146,5 @@ for iteration_number in range(1,loops+1):
|
||||
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 dft_output group of hdf5 archive in case of rerun:
|
||||
# Save stuff into the user_data group of hdf5 archive in case of rerun:
|
||||
SK.save(['chemical_potential','dc_imp','dc_energ'])
|
||||
|
||||
|
||||
@ -6,7 +6,7 @@ from pytriqs.gf.local import *
|
||||
from pytriqs.applications.dft.sumk_dft import *
|
||||
from pytriqs.applications.dft.converters.wien2k_converter import *
|
||||
|
||||
dft_filename='Gd_fcc'
|
||||
dft_filename='SrVO3'
|
||||
U = 9.6
|
||||
J = 0.8
|
||||
beta = 40
|
||||
@ -21,9 +21,14 @@ h_field = 0.0
|
||||
# Solver parameters
|
||||
p = {}
|
||||
p["max_time"] = -1
|
||||
p["length_cycle"] = 50
|
||||
p["n_warmup_cycles"] = 50
|
||||
p["n_cycles"] = 5000
|
||||
p["random_seed"] = 123 * mpi.rank + 567
|
||||
p["length_cycle"] = 200
|
||||
p["n_warmup_cycles"] = 100000
|
||||
p["n_cycles"] = 1000000
|
||||
p["perfrom_tail_fit"] = True
|
||||
p["fit_max_moments"] = 4
|
||||
p["fit_min_n"] = 30
|
||||
p["fit_max_n"] = 60
|
||||
|
||||
# If conversion step was not done, we could do it here. Uncomment the lines it you want to do this.
|
||||
#from pytriqs.applications.dft.converters.wien2k_converter import *
|
||||
@ -144,5 +149,3 @@ for iteration_number in range(1,loops+1):
|
||||
|
||||
# Save stuff into the dft_output group of hdf5 archive in case of rerun:
|
||||
SK.save(['chemical_potential','dc_imp','dc_energ'])
|
||||
|
||||
|
||||
|
||||
@ -1,6 +1,6 @@
|
||||
.. _Transport:
|
||||
|
||||
Transport calculations test
|
||||
Transport calculations
|
||||
============================
|
||||
|
||||
Formalism
|
||||
@ -44,13 +44,13 @@ real-frequency self energy by doing an analytic continuation.
|
||||
it is crucial to perform the analytic continuation in such a way that the obtained real frequency self energy
|
||||
is accurate around the Fermi energy as low energy features strongly influence the final results!
|
||||
|
||||
Besides the self energy the Wien2k files read by the transport converter (:meth:`convert_transport_input <pytriqs.applications.dft.converters.wien2k_converter.Wien2kConverter.convert_transport_input>`) are:
|
||||
Besides the self energy the Wien2k files read by the transport converter (:meth:`convert_transport_input <dft.converters.wien2k_converter.Wien2kConverter.convert_transport_input>`) are:
|
||||
* :file:`.struct`: The lattice constants specified in the struct file are used to calculate the unit cell volume.
|
||||
* :file:`.outputs`: In this file the k-point symmetries are given.
|
||||
* :file:`.oubwin`: Contains the indices of the bands within the projected subspace (written by :program:`dmftproj`) for each k-point.
|
||||
* :file:`.pmat`: This file is the output of the Wien2k optics package and contains the velocity (momentum) matrix elements between all bands in the desired energy
|
||||
window for each k-point. How to use the optics package is described below.
|
||||
* :file:`.h5`: The hdf5 archive has to be present and should contain the dft_input subgroup. Otherwise :meth:`convert_dft_input <pytriqs.applications.dft.converters.wien2k_converter.Wien2kConverter.convert_dft_input>` needs to be called before :meth:`convert_transport_input <pytriqs.applications.dft.converters.wien2k_converter.Wien2kConverter.convert_transport_input>`.
|
||||
* :file:`.h5`: The hdf5 archive has to be present and should contain the dft_input subgroup. Otherwise :meth:`convert_dft_input <dft.converters.wien2k_converter.Wien2kConverter.convert_dft_input>` needs to be called before :meth:`convert_transport_input <dft.converters.wien2k_converter.Wien2kConverter.convert_transport_input>`.
|
||||
|
||||
|
||||
Wien2k optics package
|
||||
@ -84,7 +84,7 @@ First we have to read the Wien2k files and store the relevant information in the
|
||||
|
||||
SK = SumkDFTTools(hdf_file='case.h5', use_dft_blocks=True)
|
||||
|
||||
The converter :meth:`convert_transport_input <pytriqs.applications.dft.converters.wien2k_converter.Wien2kConverter.convert_transport_input>`
|
||||
The converter :meth:`convert_transport_input <dft.converters.wien2k_converter.Wien2kConverter.convert_transport_input>`
|
||||
reads the required data of the Wien2k output and stores it in the `dft_transp_input` subgroup of your hdf file.
|
||||
Additionally we need to read and set the self energy, the chemical potential and the double counting::
|
||||
|
||||
@ -104,7 +104,7 @@ Here the transport distribution is calculated in :math:`xx` direction for the fr
|
||||
To use the previously obtained self energy we set with_Sigma to True and the broadening to :math:`0.0`.
|
||||
As we also want to calculate the Seebeck coefficient we have to include :math:`\Omega=0.0` in the mesh.
|
||||
Note that the current version of the code repines the :math:`\Omega` values to the closest values on the self energy mesh.
|
||||
For complete description of the input parameters see the :meth:`transport_distribution reference <pytriqs.applications.dft.sumk_dft_tools.SumkDFTTools.transport_distribution>`.
|
||||
For complete description of the input parameters see the :meth:`transport_distribution reference <dft.sumk_dft_tools.SumkDFTTools.transport_distribution>`.
|
||||
|
||||
The resulting transport distribution is not automatically saved, but this can be easily achieved with::
|
||||
|
||||
|
||||
@ -1,11 +1,11 @@
|
||||
.. index:: DFT Tools
|
||||
.. index:: DFTTools
|
||||
|
||||
.. module:: pytriqs.applications.dft
|
||||
|
||||
.. _dfttools:
|
||||
.. _dft:
|
||||
|
||||
DFT Tools
|
||||
=========
|
||||
DFTTools
|
||||
========
|
||||
|
||||
This :ref:`TRIQS-based <triqslibs:welcome>`-based application is aimed
|
||||
at ab-initio calculations for
|
||||
|
||||
@ -1223,9 +1223,12 @@ class SumkDFT:
|
||||
therefore calculated separately for each `k`-point.
|
||||
|
||||
Since in general n_orbitals depends on k, the calculation is done in the following order:
|
||||
..math:: n_{tot} = \sum_{k} n(k),
|
||||
with
|
||||
..math:: n(k) = Tr G_{\nu\nu'}(k, i\omega_{n}).
|
||||
|
||||
.. math:: n_{tot} = \sum_{k} n(k),
|
||||
|
||||
with
|
||||
|
||||
.. math:: n(k) = Tr G_{\nu\nu'}(k, i\omega_{n}).
|
||||
|
||||
The calculation is done in the global coordinate system, if distinction is made between local/global.
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user