worked on the sr2mgoso6 tutorial

doc/tutorials/images_scripts/Sr2MgOsO6_noSOC.indmftpr

@@ -1,5 +1,5 @@
 5                ! Nsort
-2 1 1 4 2            ! Mult(Nsort)
+2 1 1 4 2        ! Mult(Nsort)
 3                ! lmax
 complex          ! choice of angular harmonics
 0 0 0 0          ! l included for each sort
@@ -17,4 +17,4 @@ complex          ! choice of angular harmonics
 complex
 0 0 0 0
 0 0 0 0
--0.088 0.43 ! 0.40 gives warnings, 0.043 gives occ 1.996
+-0.09 0.43       

doc/tutorials/images_scripts/Sr2MgOsO6_noSOC.outdmftpr

@@ -0,0 +1,12 @@
+Density Matrices for the Correlated States :
+
+  Sort =   2  Atom =   3  and Orbital l =   2
+
+    0.000739    0.000000    0.000000    0.000000    0.000000   -0.000000   -0.000000   -0.000000    0.000000   -0.000000
+    0.000000   -0.000000    0.502746    0.000000    0.000000    0.099298    0.000000   -0.000000    0.000000   -0.000000
+    0.000000    0.000000    0.000000   -0.099298    0.020434    0.000000    0.000000   -0.000000    0.000000    0.000000
+   -0.000000    0.000000    0.000000    0.000000    0.000000    0.000000    0.735763    0.000000    0.000000    0.000000
+    0.000000    0.000000    0.000000    0.000000    0.000000   -0.000000    0.000000   -0.000000    0.735763   -0.000000
+
+The charge of the orbital is :    1.99544
+

doc/tutorials/sr2mgoso6_nosoc.rst

@@ -26,10 +26,17 @@ This is setting up a non-magnetic calculation, using the LDA and 2000 k-points i
 
   run
 
+After the SC cycled finished, you can calculate the DOS. It should look like what you can see in this figure:
+
+.. image:: images_scripts/Sr2MgOsO6_noSOC_DOS.png
+    :width: 700
+    :align: center
+
+
 Wannier orbitals
 ----------------
 
-As a next step, we calculate localised orbitals for the t2g orbitals. We use the same input file for :program:`dmftproj` as it was used in the :ref:`documentation`:
+As a next step, we calculate localised orbitals for the d orbitals. We use this input file for :program:`dmftproj`:
 
 .. literalinclude:: images_scripts/Sr2MgOsO6_noSOC.indmftpr
 
@@ -43,21 +50,60 @@ Then  :program:`dmftproj` is executed in its default mode (i.e. without spin-pol
 
    dmftproj 
 
-This program produces the necessary files for the conversion to the hdf5 file structure. This is done using
-the python module :class:`Wien2kConverter <dft.converters.wien2k_converter.Wien2kConverter>`. A simple python script that initialises the converter is::
+At the end of the run you see the density matrix in Wannier space:
+
+.. literalinclude:: images_scripts/Sr2MgOsO6_noSOC.outdmftpr
+
+As you can see, there are off-diagonal elements between the :math:`d_{x^2-y^2}` and the :math:`d_{xy}` orbital.
+
+We convert the output to the hdf5 archive, using 
+the python module :class:`Wien2kConverter <dft.converters.wien2k_converter.Wien2kConverter>`. A simple python script doing this is::
 
   from triqs_dft_tools.converters.wien2k_converter import *
   Converter = Wien2kConverter(filename = "Sr2MgOsO6_noSOC")
-
-After initializing the interface module, we can now convert the input
-text files to the hdf5 archive by::
-
   Converter.convert_dft_input()
 
 This reads all the data, and stores everything that is necessary for the DMFT calculation in the file :file:`Sr2MgOsO6_noSOC.h5`.
 
-[CONTINUE HERE]
 
 The DMFT calculation
 ====================
 
+Before starting the DMFT calculation it is beneficial to look a bit more closely at the block structure of the problem. Eventually, we want to use a basis that is as diagonal as possible, and include only the partially filled orbitals in the correlated problem. All this can be done using the functionalities of the :class:`BlockStructure <dft.block_structure.BlockStructure>` class, see section :ref:`blockstructure`.
+
+We first initialise the SumK class::
+
+    from triqs_dft_tools.sumk_dft import *
+    SK = SumkDFT(hdf_file='Sr2MgOsO6_noSOC.h5',use_dft_blocks=True)
+
+The flag *use_dft_blocks=True* determines, as usual, the smallest possible blocks with non-zero entries, and initialises them as *solver* block structure. In order to disentangle the :math:`d_{x^2-y^2}` and the :math:`d_{xy}` orbitals, and pick out only the partially filled one, we do a transformation into a basis where the local Hamiltonian is diagonal::
+
+    mat = SK.calculate_diagonalization_matrix(prop_to_be_diagonal='eal',calc_in_solver_blocks=True)
+
+We can look at the diagonalisation matrix, it is::
+
+    >>> print mat[0]['down']
+    [[ 1.   +0.j     0.   +0.j     0.   +0.j     0.   +0.j     0.   +0.j   ]
+     [ 0.   +0.j    -0.985+0.j     0.   -0.173j  0.   +0.j     0.   +0.j   ]
+     [ 0.   +0.j     0.173+0.j     0.   -0.985j  0.   +0.j     0.   +0.j   ]
+     [ 0.   +0.j     0.   +0.j     0.   +0.j     1.   +0.j     0.   +0.j   ]
+     [ 0.   +0.j     0.   +0.j     0.   +0.j     0.   +0.j     1.   +0.j   ]]
+    >>> 
+
+This transformation is already stored in the SK.block_structure class. The next step is actually not needed for a DMFT calculation, but lets see what the transformation does to the local Hamiltonian. We can calculate it before rotation, rotate it, and look at the 2x2 block with off-diagonals::
+
+    eal  = SK.eff_atomnic_levels()
+    eal2 = SK.block_structure.convert_matrix(eal[0],space_from='sumk', space_to='solver')
+
+    print eal[0]['up'][1:3,1:3]                # prints the 2x2 block with offiagonals
+    [[ 0.391+0.j    -0.   -0.815j]
+     [-0.   +0.815j  4.884-0.j   ]]
+
+    print eal2['up_1']                         # prints the 2x2 block after rotation
+    [[0.247-0.j 0.   +0.j]
+     [0.   -0.j 5.028+0.j]]
+
+So the local Hamiltonian has been diagonalised. From the other entries we can see that the *up_0* block and the [1,1] entry of the *up_1* block correspond to :math:`e_g`-like orbitals, and the others are the 
+:math:`t_{2g}` orbitals that we want to keep. 
+
+[TO BE CONTINUED...]