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Reshuffled doc on SOC and Basisrotations

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12
doc/documentation.rst
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@ -33,8 +33,16 @@ DFT+DMFT
guide/dftdmft_singleshot
guide/dftdmft_selfcons
guide/Sr2RuO4
guide/BasisRotation
Advanced Topics
---------------
.. toctree::
:maxdepth: 2
guide/basisrotation
guide/soc
guide/removeorbitals
Postprocessing
--------------

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doc/guide/BasisRotation.rst
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.. _plovasp:
.. _basisrotation:
Numerical Treatment of the Sign-Problem: Basis Rotations
=======
When performing calculations with off-diagonal complex hybridisation or local Hamiltonian, one is
often limited by the fermionic sign-problem. However, as the sign is no
physical observable, one can try to improve the calculation by rotating
to another basis.
When performing calculations with off-diagonal terms in the hybridisation function or in the local Hamiltonian, one is
often limited by the fermionic sign-problem slowing down the QMC calculations significantly. This can occur for instance if the crystal shows locally rotated or distorted cages, or when spin-orbit coupling is included. The examples for this are included in the :ref:`tutorials` of this documentation.
While the choice of basis to perform the calculation in can be chosen
arbitrarily, two choices which have shown good results are the basis
which diagonalizes the local Hamiltonian or the density matrix of then
However, as the fermonic sign in the QMC calculation is no
physical observable, one can try to improve the calculation by rotating
to another basis. While this basis can in principle be chosen arbitrarily,
two choices which have shown good results; name the basis sets that diagonalize the local Hamiltonian or the local density matrix of the
system.
The transformation matrix can be stored in the :class:`BlockStructure` and the
@ -21,7 +20,7 @@ and :meth:`put_Sigma` (see below).
Finding the Transformation Matrix
-----------------
The :class:`TransBasis` class offers a simple mehod to calculate the transformation
The :class:`TransBasis` class offers a simple method to calculate the transformation
matrices to a basis where either the local Hamiltonian or the density matrix
is diagonal::
@ -46,9 +45,10 @@ One can transform Green's functions manually using the :meth:`convert_gf` method
Automatic transformation during the DMFT loop
-----------------
During a DMFT loop one is switching back and forth between Sumk-Space and Solver-Space
in each iteration. Once the block_structure.transformation property is set, this can be
done automatically::
During a DMFT loop one is often switching back and forth between the unrotated basis (Sumk-Space) and the rotated basis that is used by the QMC Solver. However, this need not be done manually each time. Instead,
once the block_structure.transformation property is set as shown above, this is
done automatically, meaning that :class:`SumkDFT`'s :meth:`extract_G_loc`
and :meth:`put_Sigma` are doing the transformations by default::
for it in range(iteration_offset, iteration_offset + n_iterations):
# every GF is in solver space here

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doc/guide/Sr2MgOsO6/Sr2MgOsO6.indmftpr Normal file
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@ -0,0 +1,21 @@
5 ! Nsort
2 1 1 4 2 ! Mult(Nsort)
3 ! lmax
complex ! choice of angular harmonics
0 0 0 0 ! l included for each sort
0 0 0 0 ! If split into ireps, gives number of ireps. for a given orbital (otherwise 0)
cubic ! choice of angular harmonics
0 0 2 0 ! l included for each sort
0 0 0 0 ! If split into ireps, gives number of ireps. for a given orbital (otherwise 0)
0 ! SO flag
complex ! choice of angular harmonics
0 0 0 0 ! l included for each sort
0 0 0 0 ! If split into ireps, gives number of ireps. for a given orbital (otherwise 0)
complex ! choice of angular harmonics
0 0 0 0 ! l included for each sort
0 0 0 0 ! If split into ireps, gives number of ireps. for a given orbital (otherwise 0)
complex
0 0 0 0
0 0 0 0
-0.088 0.43 ! 0.40 gives warnings, 0.043 gives occ 1.996
0.04301

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doc/guide/Sr2MgOsO6/Sr2MgOsO6.struct Normal file
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@ -0,0 +1,72 @@
Sr2MgOsO6 s-o calc. M|| 0.00 0.00 1.00
B 5 87
RELA
10.507954 10.507954 14.968880 90.000000 90.000000 90.000000
ATOM -1: X=0.00000000 Y=0.50000000 Z=0.75000000
MULT= 2 ISPLIT=-2
-1: X=0.50000000 Y=0.00000000 Z=0.75000000
Sr 2+ NPT= 781 R0=.000010000 RMT= 2.50000 Z: 38.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -2: X=0.00000000 Y=0.00000000 Z=0.00000000
MULT= 1 ISPLIT=-2
Os 6+ NPT= 781 R0=.000005000 RMT= 1.94 Z: 76.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -3: X=0.00000000 Y=0.00000000 Z=0.50000000
MULT= 1 ISPLIT=-2
Mg 2+ NPT= 781 R0=.000100000 RMT= 1.89 Z: 12.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -4: X=0.74270000 Y=0.21790000 Z=0.00000000
MULT= 4 ISPLIT= 8
-4: X=0.25730000 Y=0.78210000 Z=0.00000000
-4: X=0.21790000 Y=0.25730000 Z=0.00000000
-4: X=0.78210000 Y=0.74270000 Z=0.00000000
O 2- NPT= 781 R0=.000100000 RMT= 1.58 Z: 8.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -5: X=0.00000000 Y=0.00000000 Z=0.75390000
MULT= 2 ISPLIT=-2
-5: X=0.00000000 Y=0.00000000 Z=0.24610000
O 2- NPT= 781 R0=.000100000 RMT= 1.58 Z: 8.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
8 NUMBER OF SYMMETRY OPERATIONS
0-1 0 0.00000000
1 0 0 0.00000000
0 0-1 0.00000000
1
-1 0 0 0.00000000
0-1 0 0.00000000
0 0-1 0.00000000
2
1 0 0 0.00000000
0 1 0 0.00000000
0 0-1 0.00000000
3
0-1 0 0.00000000
1 0 0 0.00000000
0 0 1 0.00000000
4
0 1 0 0.00000000
-1 0 0 0.00000000
0 0-1 0.00000000
5
-1 0 0 0.00000000
0-1 0 0.00000000
0 0 1 0.00000000
6
1 0 0 0.00000000
0 1 0 0.00000000
0 0 1 0.00000000
7
0 1 0 0.00000000
-1 0 0 0.00000000
0 0 1 0.00000000
8

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doc/guide/Sr2MgOsO6/Sr2MgOsO6_SOC.indmftpr Normal file
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@ -0,0 +1,21 @@
5 ! Nsort
2 1 1 4 2 ! Mult(Nsort)
3 ! lmax
complex ! choice of angular harmonics
0 0 0 0 ! l included for each sort
0 0 0 0 ! If split into ireps, gives number of ireps. for a given orbital (otherwise 0)
cubic ! choice of angular harmonics
0 0 2 0 ! l included for each sort
0 0 0 0 ! If split into ireps, gives number of ireps. for a given orbital (otherwise 0)
1 ! SO flag
complex ! choice of angular harmonics
0 0 0 0 ! l included for each sort
0 0 0 0 ! If split into ireps, gives number of ireps. for a given orbital (otherwise 0)
complex ! choice of angular harmonics
0 0 0 0 ! l included for each sort
0 0 0 0 ! If split into ireps, gives number of ireps. for a given orbital (otherwise 0)
complex
0 0 0 0
0 0 0 0
-0.088 0.43 ! 0.40 gives warnings, 0.043 gives occ 1.996
0.04301

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doc/guide/Sr2RuO4.rst
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@ -1,40 +0,0 @@
.. _Sr2RuO4:
Spin-orbit coupled calculations (single-shot)
=============================================
There are two main ways of including the spin-orbit coupling (SO) term into
DFT+DMFT calculations:
- by performing a DFT calculation including SO and then doing a DMFT calculation on top, or
- by performing a DFT calculation without SO and then adding the SO term on the model level.
Treatment of SO in DFT
----------------------
For now, TRIQS/DFTTools does only work with Wien2k when performing calculations with SO.
Of course, the general Hk framework is also possible.
But the way VASP treats SO is fundamentally different to the way Wien2k treats it and the interface does not handle that at the moment.
Therefore, this guide assumes that Wien2k is being used.
First, a Wien2k calculation including SO has to be performed.
For details, we refer the reader to the documentation of Wien2k.
The interface to Wien2k only works when the DFT calculation is done both spin-polarized and with SO (that means that you have to initialize the Wien2k calculation accordingly and then run with ``runsp -sp``).
Performing the projection
~~~~~~~~~~~~~~~~~~~~~~~~~
Note that the final ``x lapw2 -almd -so -up`` and ``x lapw2 -almd -so -dn`` have to be run *on a single core*, which implies that, before, ``x lapw1 -up``, ``x lapw2 -dn``, and ``x lapwso -up`` have to be run in single-core mode (once).
In the ``case.indmftpr`` file, the spin-orbit flag has to be set to ``1`` for the correlated atoms.
For example, for the compound Sr\ :sub:`2`\ RuO\ :sub:`4`, with the struct file :download:`Sr2RuO4.struct <Sr2RuO4/Sr2RuO4.struct>`, we would e.g. use the ``indmftpr`` file :download:`found here <Sr2RuO4/Sr2RuO4.indmftpr>`.
Then, ``dmftproj -sp -so`` has to be called.
As usual, it is important to check for warnings (e.g., about eigenvalues of the overlap matrix) in the output of ``dmftproj`` and adapt the window until these warnings disappear.
Note that in presence of SO, it is not possible to project only onto the :math:`t_{2g}` subshell because it is not an irreducible representation.
A redesign of the orthonormalization procedure might happen in the long term, which might allow that.
We strongly suggest using the :py:meth:`.dos_wannier_basis` functionality of the :py:class:`.SumkDFTTools` class (see :download:`calculate_dos_wannier_basis.py <Sr2RuO4/calculate_dos_wannier_basis.py>`) and compare the Wannier-projected orbitals to the original DFT DOS (they should be more or less equal).
Note that, with SO, there are usually off-diagonal elements of the spectral function, which can also be imaginary.
The imaginary part can be found in the third column of the files ``DOS_wann_...``.

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.. _removeorbitals:
Reducing the number of orbitals for the Solver
==============================================
To be done...

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.. _soc:
Spin-orbit coupled calculations (single-shot)
=============================================
There are two main ways of including the spin-orbit coupling (SOC) term into
DFT+DMFT calculations:
- by performing a DFT calculation including SOC and then doing a DMFT calculation on top, or
- by performing a DFT calculation without SOC and then adding the SOC term on the model level.
Treatment of SOC in DFT
-----------------------
For now, TRIQS/DFTTools does only work with Wien2k when performing calculations with SO.
The treatment of SOC in the VASP package is fundamentally different to the way Wien2k treats it, and the interface does not handle that at the moment.
Therefore, this guide describes how to do an AOC calculation using the Wien2k DFT package.
First, a Wien2k calculation including SOC has to be performed.
For details, we refer the reader to the documentation of Wien2k. As a matter of fact, we need the output for the DFT band structure for both spin directions explicitly. That means that one needs to do a spin-polarised DFT calculation with SOC, but, however, with magnetic moment set to zero. In the Wien2k initialisation procedure, one can choose for the option -nom when ``lstart`` is called. This means that the charge densities are initialised without magnetic splitting. The SOC calculation is then performed in a standard way as described in the Wien2k manual.
Performing the projection
~~~~~~~~~~~~~~~~~~~~~~~~~
Note that the final ``x lapw2 -almd -so -up`` and ``x lapw2 -almd -so -dn`` have to be run *on a single core*, which implies that, before, ``x lapw2 -up``, ``x lapw2 -dn``, and ``x lapwso -up`` have to be run in single-core mode (at least once).
In the ``case.indmftpr`` file, the spin-orbit flag has to be set to ``1`` for the correlated atoms.
For example, for the compound Sr\ :sub:`2`\ MgOsO\ :sub:`6`, with the struct file :download:`Sr2MgOsO6.struct <Sr2MgOsO6/Sr2MgOsO6.struct>`, we would, e.g., use the ``indmftpr`` file :download:`found here <Sr2MgOsO6/Sr2MgOsO6_SOC.indmftpr>`.
Then, ``dmftproj -sp -so`` has to be called.
As usual, it is important to check for warnings (e.g., about eigenvalues of the overlap matrix) in the output of ``dmftproj`` and adapt the window until these warnings disappear.
Note that in presence of SOC, it is not possible to project only onto the :math:`t_{2g}` subshell because it is not an irreducible representation.
We strongly suggest using the :py:meth:`.dos_wannier_basis` functionality of the :py:class:`.SumkDFTTools` class (see :download:`calculate_dos_wannier_basis.py <Sr2RuO4/calculate_dos_wannier_basis.py>`) and compare the Wannier-projected orbitals to the original DFT DOS (they should be more or less equal).
Note that, with SOC, there are usually off-diagonal elements of the spectral function, which can also be imaginary.
The imaginary part can be found in the third column of the files ``DOS_wann_...``.
After the projection, one can proceed with the DMFT calculation. However, two things need to be noted here. First, since the spin is not a good quantum number any more, there are off-diagonal elements in the hybridisation function and the local Hamiltonian coupling the two spin directions. This will eventually lead to a fermonic sign problem when QMC is used as a impurity solver. Second, although the :math:`e_{g}` subshell needs to be included in the projection, it can in many cases be neglected in the solution of the Anderson impurity model, after a transformation to a rotated local basis is done. This basis diagonalising the local Hamiltonian in the presence of SOC, is often called the numerical j-Basis. How rotations are performed is described in :ref:`basisrotation`, and the cutting of the orbitals in :ref:`removeorbitals`.
A DMFT calculation including SOC for Sr2MgOsO6 is included in the :ref:`tutorials`.