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<div id="content">
<h1 class="title">ecalj: MTO-based effective Hamiltonian Project.</h1>
<div id="table-of-contents">
<h2>Table of Contents</h2>
<div id="text-table-of-contents">
<ul>
<li><a href="#orgbe3687b">1. CAUTION</a></li>
<li><a href="#org7b5cd90">2. step1: Get rst (and/or sigm).</a></li>
<li><a href="#org6803350">3. step2: Band plot with APW+MTO</a></li>
<li><a href="#org6575ad3">4. step3: Band Plot with MTO only</a></li>
<li><a href="#org4d038f7">5. step4: Generate PMT Hamiltonian for all mesh points.</a></li>
<li><a href="#orge59f1fc">6. step 5: Run lmfham1 and Read lm7K/lmfham1.F</a></li>
<li><a href="#orgf9e798c">7. Plan for development. -------------</a></li>
</ul>
</div>
</div>
<p>
This file is written in org-mode in emacs.
</p>

<p>
Here we show how to get MTO-only Hamiltonian after you get convergence in the PMT=MTO+APW method.
Examples are in Si_HamMTO, Fe_HamMTO. Follow instructions below at first.
</p>


<div id="outline-container-orgbe3687b" class="outline-2">
<h2 id="orgbe3687b"><span class="section-number-2">1</span> CAUTION</h2>
<div class="outline-text-2" id="text-1">
<ul class="org-ul">
<li>iprint=0 except master in bndfp.F 
To supress output except master, I have a line in bndfp.F as</li>
</ul>
<pre class="example">
ipr=iprint() !When procid/=master, iprint=0
</pre>

<p>
. So, what is done in other nodes are not shown.
</p>


<ul class="org-ul">
<li>We now use pwmode=1 (but =11 should work as well).</li>

<li>Spin symmetric MTOs with &#x2013;phispinsym.</li>
</ul>
<p>
This is implmented in 
</p>
<pre class="example">
commit c81819cc16fd34d4bb352ba2eb9dc3e1d354aa56
</pre>

<p>
Its log says 
</p>

<pre class="example">
Author: Takao Kotani &lt;takaokotani@gmail.com&gt;
Date:   Tue Aug 27 12:36:50 2019 +0900
   
    With --phispinsym option for lmf,lmf-MPIK, we can use spin-averages pnu and V0.
    You can use job_ham_phispinsym instead of job_ham.
    
    From V0 and pnu, we calculate radial funcitons phi and phidot.
       pnu corresponding to energies of radial schrodinger eq.
       V0 is the spherical potential, ssite(ib)%rv_a_ov0.
    
    
    Search --phispinsym in the console output. It shows
    ----
     bndfp: --phispinsym use spin-averaged potential for phi and phidot
      ibas l=  1  0 pnu=   4.58531   4.57791 --&gt;   4.58161
      ibas l=  1  1 pnu=   4.40324   4.38211 --&gt;   4.39268
    .... (this is symmetrization of pnu) at the begining of bndfp
    ----
     locpot: --phispinsym mode: use spin-averaged potential for phi and phidot
      ibas l=  1  0 pnu(1:nsp) pnz(1:nsp)=   4.58161   4.58161   0.00000   0.00000
      ibas l=  1  1 pnu(1:nsp) pnz(1:nsp)=   4.39268   4.39268   3.94432   3.94432
    ... (this shows pnu used in locpot).
    
    What we can do are
    
    1. self-consistent calculations can be performed with --phispinsym
    
    2. Even if the self-consistency is spin-dependent phi,phidot,
       job_ham_phispinsym (see --phispinsym option) gives Hamiltonian, based on the spin-symmetric radial functions.
       Then the radial functions are calculated from the spin-averaged V0 and pnu.
    ---
    I think we can perfrom QSGW calculation if we use the option for lmf,lmfgw
       (not tested yet). We may need to insert --phispinsym in gwsc script (not yet).
    I think we can give Hamiltonian based on the spin-averaged phi,phidot
       even in QSGW self-consistent results without --phispinsym.
    
    =====================================================================
    MEMO for development:
     =====================================================================
    At first, note that we have lmf subroutines;
    --------
    fp/bndfp.F (main one-iteration loop of band calculation)
      -mkpot (potential generation)
      --locpot (MT parts)
      ---augmat (augmentation matrix: MT-part of Hamiltonian and overlap matrix).
    Note mkpot is called even in bndfp-sugw-mkpot
    
    locpot: gives ov0. ov0 is symmetrized.
    pnunew: renew pnu---so pnu should symmetrized.
    bndfp:  pnu is symmetrized at the begining befor mkpot-locpot
</pre>
</div>
</div>



<div id="outline-container-org7b5cd90" class="outline-2">
<h2 id="org7b5cd90"><span class="section-number-2">2</span> step1: Get rst (and/or sigm).</h2>
<div class="outline-text-2" id="text-2">
<p>
From ctrl.si (or others like ctrl.fe), you do self-consistent calculations.
Check pwmode=1 as 
% const pwmode=1
      PWMODE={pwmode} 
in ctrl file
</p>

<div class="org-src-container">
<pre class="src src-bash">lmfa fe
lmf fe
</pre>
</div>
<p>
It can be LDA or QSGW, final results are in
rst.fe (sigm.fe in QSGW in addition to this).
</p>
</div>
</div>


<div id="outline-container-org6803350" class="outline-2">
<h2 id="org6803350"><span class="section-number-2">3</span> step2: Band plot with APW+MTO</h2>
<div class="outline-text-2" id="text-3">
<p>
Make band plot. We need syml.fe or syml.si
(you can get it by &gt;getsylm fe; getsyml need to be soft linked to ecalj/GetSyml/getsyml.py).
</p>
<pre class="example">
job_band fe -np 24, or si
</pre>


<p>
In llmf_band, you can find following lines  at
</p>
<pre class="example">
bndfp: kpt     2 of    97 k=  0.0000 -0.0500  0.0000 ndimh = nmto+napw =    41   28   13
</pre>

<p>
This means 28 MTOs and 13 APWs used.
Try
</p>
<pre class="example">
&gt;grep bndfp nmto fe
</pre>

<p>
Note job_band does not change rst file.
</p>

<p>
Keep your band plot. For example,
</p>
<pre class="example">
&gt;mkdir PWMODE1
&gt;cd PWMODE1
&gt;cp bandplot* PWMODE1
&gt;cp bnd* PWMODE1
</pre>

<p>
You can replot bands by 
</p>
<pre class="example">
&gt;cd PWMODE1
&gt;gnuplot -p bandplot.isp1.glt
</pre>


<p>
Current version of band mode generates qplist.dat which contains q point llist for band plot.
</p>

<p>
NOTE: Eigenvalues are written as (in Ry)
</p>
<pre class="example">
bndfp: kpt    1 of   97 k jsp=  0.00000  0.00000  0.00000 2 nev=   34
-3.7314 -3.7314 -3.7314 -0.5675 -0.0092 -0.0091 -0.0091  0.1240  0.1240
 1.7952  1.7952  1.7952  2.4145  2.4145  2.4311  2.4311  2.4312  3.1464
 3.1465  3.1465  3.7662  4.7800  4.7801  4.7801  6.2200  6.2204  6.3346
 6.4887  7.3912  7.3913  7.3914  8.3638  8.3642  8.3648
</pre>
</div>
</div>



<div id="outline-container-org6575ad3" class="outline-2">
<h2 id="org6575ad3"><span class="section-number-2">4</span> step3: Band Plot with MTO only</h2>
<div class="outline-text-2" id="text-4">
<pre class="example">
&gt; job_band si -np 4 -vpwmode=0
</pre>


<p>
Check 'calculations without APW' are good enough or not. (superpose bands in the step2 and step3.)
(energy bands are plotted by the gnuplot script bandplot.isp*.glt)
</p>

<p>
In the case of Si, a little differnce between PMT=APW+MTO and MTO-only.
Without APWs, we have Band gap is too large by &sim; 0.2eV in the case of pwmode=0.
(one reason is that we use very localize MTOs in the default setting. or no empty spheres)
</p>

<p>
Keep your band plot. For example,
</p>
<pre class="example">
&gt;mkdir PWMODE0
&gt;cd PWMODE0
&gt;cp bandplot* PWMODE0
&gt;cp bnd* PWMODE01
</pre>

<p>
You can replot bands by 
</p>
<pre class="example">
&gt;cd PWMODE0
&gt;gnuplot -p bandplot.isp1.glt
</pre>


<p>
You can compare two band plot with -vpmode=1 and -vpmode=0 by a gnuplot command as follows.
gnuplot commands can be
</p>
<pre class="example">
plot \
"PWMODE0/bnd001.spin1" u ($2):($3) lt 1 pt 1 w lp,\
"PWMODE0/bnd002.spin1" u ($2):($3) lt 1 pt 1 w lp,\
"PWMODE0/bnd003.spin1" u ($2):($3) lt 1 pt 1 w lp,\
"PWMODE0/bnd004.spin1" u ($2):($3) lt 1 pt 1 w lp,\
"PWMODE0/bnd005.spin1" u ($2):($3) lt 1 pt 1 w lp,\
"PWMODE0/bnd006.spin1" u ($2):($3) lt 1 pt 1 w lp,\
"PWMODE1/bnd001.spin1" u ($2):($3) lt 2 pt 2 w lp,\
"PWMODE1/bnd002.spin1" u ($2):($3) lt 2 pt 2 w lp,\
"PWMODE1/bnd003.spin1" u ($2):($3) lt 2 pt 2 w lp,\
"PWMODE1/bnd004.spin1" u ($2):($3) lt 2 pt 2 w lp,\
"PWMODE1/bnd005.spin1" u ($2):($3) lt 2 pt 2 w lp,\
"PWMODE1/bnd006.spin1" u ($2):($3) lt 2 pt 2 w lp
pause -1
</pre>
<p>
(you can see the difference in ecalj/MATERIALS/Si_HamMTO/SiPWMODE11vs0.png)
</p>


<p>
At this point, you can check discrapancy between PMT=MTO+APW and MTO-block only diagonalization.
</p>
</div>
</div>


<div id="outline-container-org4d038f7" class="outline-2">
<h2 id="org4d038f7"><span class="section-number-2">5</span> step4: Generate PMT Hamiltonian for all mesh points.</h2>
<div class="outline-text-2" id="text-5">
<pre class="example">
&gt;job_ham si -np 24 -np 4
</pre>

<p>
See job_ham script.
HamiltonianPMT contains Hamiltonian and ovarlap matrix in the 1st BZ.
In the job_ham script, we use full mesh option &#x2013;fullmesh, which means we calculate 
Hamiltonian of all mesh points, e.g. 64 k point for 4x4x4. IF -np 4, only eigenvalues 64/4=16 k 
points are shown in the console output( In bndfp.F, we plot only the output of master core).
</p>

<p>
Be careful. At the begining of job_ham, we calculate the fermi energy by
&gt;mpirun -np $3 ~/ecalj/lm7K/lmf-MPIK $1 &#x2013;quit=band &gt; lmf_efermi
This generate fermi energy file efermi.lmf.
This is for default pwmode if you don't specify -vpwmode=1.
</p>
</div>
</div>


<div id="outline-container-orge59f1fc" class="outline-2">
<h2 id="orge59f1fc"><span class="section-number-2">6</span> step 5: Run lmfham1 and Read lm7K/lmfham1.F</h2>
<div class="outline-text-2" id="text-6">
<p>
lmfham1 read <code>HamltonianPMT</code> and <code>HamiltonianPMTinfo</code>.
Here HamiltonianPMT contains the Hamiltonian and overlap matrix for MTO+APW.
Look into ecalj/lm7K/lmfham1.F
</p>

<p>
You can run lmfham1 only from files
</p>
<pre class="example">
HamiltonianPMT     (hamiltonian and overlap matrix)
HamiltonianPMTinfo (info lf lattice and  index 
qplits.dat         (qpoint for which we plot bands).
</pre>

<p>
(For example, you put only these files in a directory and run lmfham1)
Run 
</p>
<pre class="example">
&gt;lmfham1
</pre>

<p>
lmfham1 generetes HamiltonianMTO and overlap matrix, and diagonalize it.
You have to read ecalj/lm7K/lmfham1.F
</p>

<p>
This generates "band_lmfham_spin1.dat" (and band_lmfham_spin2.dat for isp=2).
To plot them, use gnuplot scipt such as
</p>
<pre class="example">
ef=0.2239816400'                                     
plot \'                                              
"bnd001.spin1" u ($2):($3) lt 1 pt 1 w lp,\'         
"bnd002.spin1" u ($2):($3) lt 1 pt 1 w lp,\'         
"bnd003.spin1" u ($2):($3) lt 1 pt 1 w lp,\'         
"bnd004.spin1" u ($2):($3) lt 1 pt 1 w lp,\'         
"bnd005.spin1" u ($2):($3) lt 1 pt 1 w lp,\'         
"bnd006.spin1" u ($2):($3) lt 1 pt 1 w lp,\'         
"band_lmfham_spin1.dat" u ($1):(13.605*($2-ef)) pt 2'
</pre>
<p>
Here we need to set Fermi energy <code>ef</code>. See L1:qplist.dat to take the Fermi energy for temporay use.
L1:qpllist.dat is the fermi energy (top of valence) from your last run of job_band).
(this is shown at the end of console output of lmfham1 for convenience).
</p>

<p>
In future, fermi energy should be determined within lmfham1.
</p>

<ul class="org-ul">
<li>The PMT index is shown in the console output of lmfham1.F
Do
&gt;lmfham1 |grep MHAM
It shows the Hamiltonian index corresponds to which PMTs.</li>
</ul>

<p>
&#x2014;
In lmfham1.F, we read HamiltonianPMT and HamitonianPMTinfo by call ReadHamPMTinfo(),
Then we generate real-space Hamiltonian and Ovelap for MTO only by call HamPMTtoHamRsMTO, which
results in a file HamRsMTO.
This is readin by call ReadHamRsMTO(). 
NOTE: for separation in future, we write and read HamRsMTO in lmfham1.
</p>

<p>
Then, mainly in the main routine in lmfham1.F, we generate hamm, for k along the k points on symmetry line.
See the current version of lmfham1.F is with symlcase=.true (you may modify this to any k points).
And then diagonalize it by "call zhev_tk2" 
(the subroutine's main inputs are hamm and ovlm, epsovl is for removing basis with poor linear dependency).
</p>

<p>
The index of PMT basis is included in HamiltonianPMTInfo. 
See m_readhamiltonianPMT in lmfham1.F.
</p>
<ul class="org-ul">
<li>ldim: Hamiltonian dimension</li>
<li>ib_table: site index (site ordering is shown by lmchk).</li>
<li>l_tabale: l table. m takes -l to l ordering. See ends of jobpdos (showing real space harmonics).</li>
<li>k_table: k takes 1(EH),2(EH2), or 3(LO).</li>
</ul>
<p>
Ask to takaokotani@gmail.com 
</p>
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<div id="outline-container-orgf9e798c" class="outline-2">
<h2 id="orgf9e798c"><span class="section-number-2">7</span> Plan for development. -------------</h2>
<div class="outline-text-2" id="text-7">
<p>
We have to modify HamPMTtoHamRsMTO().
which is including the energy correction.
That is, 
</p>
<hr />
<p>
From Hij(k)^PMT and Oij(k)^PMT,
we have to generates Hij(k)^MTO and Oij(k)^MTO.
(we don't need to touch conversion part from k to real). 
In the current vertion, we simply take the MTO block of PMT Hamiltonians.
In the next vertion,
  Hij(k)^PMT &#x2013;&gt; Hij(k)^MTO
should be corrected.
</p>
<hr />
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<div id="postamble" class="status">
<p class="author">Author: takao kotani @ tottori university, Japan</p>
<p class="date">Created: 2019-11-11 月 16:03</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
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