Reshuffled doc on SOC and Basisrotations

doc/documentation.rst

@@ -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
 --------------

doc/guide/BasisRotation.rst

@@ -1,16 +1,15 @@
-.. _plovasp:
+.. _basisrotation:
 
 Numerical Treatment of the Sign-Problem: Basis Rotations
 =======
 
-When performing calculations with off-diagonal complex hybridisation or local Hamiltonian, one is
+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. However, as the sign is no
+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.
-physical observable, one can try to improve the calculation by rotating
-to another basis.
 
-While the choice of basis to perform the calculation in can be chosen
+However, as the fermonic sign in the QMC calculation is no
-arbitrarily, two choices which have shown good results are the basis
+physical observable, one can try to improve the calculation by rotating
-which diagonalizes the local Hamiltonian or the density matrix of then
+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
+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, 
-in each iteration. Once the block_structure.transformation property is set, this can be
+once the block_structure.transformation property is set as shown above, this is
-done automatically::
+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

doc/guide/Sr2MgOsO6/Sr2MgOsO6.indmftpr

@@ -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

doc/guide/Sr2MgOsO6/Sr2MgOsO6.struct

@@ -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

doc/guide/Sr2MgOsO6/Sr2MgOsO6_SOC.indmftpr

@@ -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

doc/guide/Sr2RuO4.rst

@@ -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_...``.

doc/guide/removeorbitals.rst

@@ -0,0 +1,6 @@
+.. _removeorbitals:
+
+Reducing the number of orbitals for the Solver
+==============================================
+
+To be done...

doc/guide/soc.rst

@@ -0,0 +1,41 @@
+.. _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`.