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173 lines
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ReStructuredText
173 lines
9.7 KiB
ReStructuredText
.. _convW90:
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Interface with Wannier90
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========================
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This interface allows to convert the output of `wannier90 <http://wannier.org>`_
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Maximally Localized Wannier Functions (MLWF) and create a HDF5 archive suitable for DMFT calculations with the
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:class:`SumkDFT <dft.sumk_dft.SumkDFT>` class. The tasks are parallelized with MPI.
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The converter can be run in two different modes, which are specified with the keyword ``bloch_basis`` in the call::
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from triqs_dft_tools.converters import Wannier90Converter
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Converter = Wannier90Converter(seedname='seedname', bloch_basis=False, rot_mat_type='hloc_diag', add_lambda=None)
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Here and in the following, the keyword ``seedname`` should always be intended
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as a placeholder for the actual prefix chosen by the user when creating the
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input for :program:`wannier90`.
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Orbital mode
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---------------
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In the default mode (``bloch_basis = False``), the Converter writes the Hamiltonian in orbital basis, in which case
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the projector functions are trivial identity matrices. The user must supply two files:
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#. The file :file:`seedname_hr.dat`, which contains the DFT Hamiltonian
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in the MLWF basis calculated through :program:`wannier90` with ``write_hr = true``
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(please refer to the :program:`wannier90` documentation).
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#. A file named :file:`seedname.inp`, which contains the required
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information about the :math:`\mathbf{k}`-point mesh, the electron density,
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the correlated shell structure, ... (see below).
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Once these two files are available, one can use the converter as follows::
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Converter.convert_dft_input()
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The converter input :file:`seedname.inp` is a simple text file with
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the following format:
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.. literalinclude:: images_scripts/LaVO3_w90.inp
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The example shows the input for the perovskite crystal of LaVO\ :sub:`3`
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in the room-temperature `Pnma` symmetry. The unit cell contains four
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symmetry-equivalent correlated sites (the V atoms) and the total number
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of electrons per unit cell is 8 (see second line).
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The first line specifies how to generate the :math:`\mathbf{k}`-point
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mesh that will be used to obtain :math:`H(\mathbf{k})`
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by Fourier transforming :math:`H(\mathbf{R})`.
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Currently implemented options are:
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* :math:`\Gamma`-centered uniform grid with dimensions
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:math:`n_{k_x} \times n_{k_y} \times n_{k_z}`;
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specify ``0`` followed by the three grid dimensions,
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like in the example above
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* :math:`\Gamma`-centered uniform grid with dimensions
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automatically determined by the converter (from the number of
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:math:`\mathbf{R}` vectors found in :file:`seedname_hr.dat`);
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just specify ``-1``
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Inside :file:`seedname.inp`, it is crucial to correctly specify the
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correlated shell structure, which depends on the contents of the
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:program:`wannier90` output :file:`seedname_hr.dat` and on the order
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of the MLWFs contained in it. In this example we have four lines for the
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four V atoms. The MLWFs were constructed for the t\ :sub:`2g` subspace, and thus
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we set ``l`` to 2 and ``dim`` to 3 for all V atoms. Further the spin-orbit coupling (``SO``)
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is set to 0 and ``irep`` to 0.
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As in this example all 4 V atoms are equivalent we set ``sort`` to 0. We note
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that, e.g., for a magnetic DMFT calculation the correlated atoms can be made
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inequivalent at this point by using different values for ``sort``.
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The number of MLWFs must be equal to, or greater than the total number
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of correlated orbitals (i.e., the sum of all ``dim`` in :file:`seedname.inp`).
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If the converter finds fewer MLWFs inside :file:`seedname_hr.dat`, then it
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stops with an error; if it finds more MLWFs, then it assumes that the
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additional MLWFs correspond to uncorrelated orbitals (e.g., the O-\ `2p` shells).
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When reading the hoppings :math:`\langle w_i | H(\mathbf{R}) | w_j \rangle`
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(where :math:`w_i` is the :math:`i`-th MLWF), the converter also assumes that
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the first indices correspond to the correlated shells (in our example,
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the V-t\ :sub:`2g` shells). Therefore, the MLWFs corresponding to the
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uncorrelated shells (if present) must be listed **after** those of the
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correlated shells.
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With the :program:`wannier90` code, this can be achieved by listing the
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projections for the uncorrelated shells after those for the correlated shells.
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In our `Pnma`-LaVO\ :sub:`3` example, for instance, we could use::
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Begin Projections
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V:l=2,mr=2,3,5:z=0,0,1:x=-1,1,0
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O:l=1:mr=1,2,3:z=0,0,1:x=-1,1,0
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End Projections
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where the ``x=-1,1,0`` option indicates that the V--O bonds in the octahedra are
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rotated by (approximatively) 45 degrees with respect to the axes of the `Pbnm` cell.
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The last line of :file:`seedname.inp` is the DFT Fermi energy (in eV), which is subtracted from the onsite
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terms in the :file:`seedname_hr.dat` file. This is recommended since some functions in DFTTools implicitly
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assume a Fermi energy of 0 eV.
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In the orbital mode the Converter supports the addition of a local spin-orbit term, if the Wannier Hamiltonian
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describes a t\ :sub:`2g` manifold. Currently, the correct interaction term is only implemented if the default
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orbital order of :program:`wannier90` is maintained, i.e. it is assumed to be
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:math:`d_{xz,\uparrow}, d_{yz,\uparrow}, d_{xy,\uparrow}, d_{xz,\downarrow}, d_{yz,\downarrow}, d_{xy,\downarrow}`.
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The coupling strength can be specified as ``add_lambda = [lambda_x, lambda_y, lambda_z]``,
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representative of the orbital coupling terms perpendicular to :math:`[x, y, z]` i.e. :math:`[d_{yz}, d_{xz}, d_{xy}]`,
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respectively. Note that it is required to have ``SO=0`` and ``SP=1``.
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For spin-orbit coupled systems (from DFT or with the add_lambda parameter),
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the orbitals are resorted internally by the converter to the triqs order so, e.g.,
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the order from above would become
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:math:`d_{xz,\uparrow}, d_{xz,\downarrow}, d_{yz,\uparrow}, d_{yz,\downarrow}, d_{xy,\uparrow}, d_{xy,\downarrow}`.
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Band mode
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----------------
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If ``bloch_basis = True``, the Converter writes the Hamiltonian in the Kohn-Sham basis that was used to construct
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the Wannier functions. The projector functions are then given by the transformation from Kohn-Sham to orbital basis.
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Note that to do so :program:`wannier90` must be run with ``write_u_matrices = true``. Additionally to the files
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described above, the Converter will require the following files:
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#. :file:`seedname_u.mat` (and :file:`seedname_u_dis.mat` if disentanglement was used to construct the Wannier functions.) is read to construct the projector functions.
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#. :file:`seedname.eig` is read to get the Kohn-Sham band eigenvalues
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#. :file:`seedname.nnkp` is read to obtain the band indices of the orbitals selected for the Wannier Hamiltonian
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#. :file:`seedname.wout` is read to get the outer energy window to ensure the correct mapping of the disentanglement
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Note that in case of disentanglement the user must set the outer energy window (``dis_win_min`` and ``dis_win_max``) explicitly in :program:`wannier90` with an energy
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separation of at least :math:`10^{-4}` to the band energies. This means in particular that one should not use the default energy window to avoid subtle bugs.
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Additionally, to keep the dimension of the lattice Green's function reasonable, it is recommendable to use the exclude_bands tag for bands completely outside of the energy window.
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The Converter currently works with Quantum Espresso and VASP. Additional files are required for each case to obtain
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the Fermi weights:
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#. :file:`seedname.nscf.out` for Quantum Espresso (the NSCF run must contain the flag ``verbosity = 'high'``)
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#. :file:`OUTCAR` and :file:`LOCPROJ` for VASP
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Note that in the band mode the user input of the :math:`k`-mesh and the Fermi energy in :file:`seedname.inp` are ignored, since both quantities
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are automatically read from the :program:`wannier90` and DFT output. However, the :math:`k`-mesh parameter still has to be specified to comply with the file format.
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Rotation matrix
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------------------
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The converter will analyse the matrix elements of the local Hamiltonian
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to find the symmetry matrices `rot_mat` needed for the global-to-local
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transformation of the basis set for correlated orbitals
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(see section :ref:`hdfstructure`).
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If ``rot_mat_type='hloc_diag'``, the matrices are obtained by finding the unitary transformations that diagonalize
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:math:`\langle w_i | H_I(\mathbf{R}=0,0,0) | w_j \rangle`, where :math:`I` runs
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over the correlated shells and `i,j` belong to the same shell (more details elsewhere...).
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If ``rot_mat_type='wannier'``, the matrix for the first correlated shell per impurity will be identity, defining the reference frame,
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while the rotation matrices of all other equivalent shells contain the correct mapping into this reference frame.
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If two correlated shells are defined as equivalent in :file:`seedname.inp`,
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then the corresponding eigenvalues have to match within a threshold of 10\ :sup:`-5`,
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otherwise the converter will produce an error/warning.
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If this happens, please carefully check your data in :file:`seedname_hr.dat`.
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This method might fail in non-trivial cases (i.e., more than one correlated
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shell is present) when there are some degenerate eigenvalues:
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so far tests have not shown any issue, but one must be careful in those cases
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(the converter will print a warning message and turns off the use of rotation matrices,
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which leads to an incorrect mapping between equivalent correlated shells).
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Note that in the case of spin-orbit coupling, these rotation matrices in general
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mix spin and orbital components.
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Current limitations
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----------------------------------------------
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The current implementation of the Wannier90 Converter has some limitations:
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* Since :program:`wannier90` does not make use of symmetries (symmetry-reduction
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of the :math:`\mathbf{k}`-point grid is not possible), the converter always
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sets ``symm_op=0`` (see the :ref:`hdfstructure` section).
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* The spin-polarized case (``SP=1``) is neither completely implemented nor tested.
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* ``proj_mat_all`` are not used, so there are no projectors onto the
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uncorrelated orbitals for now.
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