[Wannier] different initial projection get same wannierisation result, however, the hr.dat has significant imaginary part for many situation

[Mostofi, Arash]

Dear Wannier90 user,

One of the conventions for the use of this mailing list is to sign with your name and affiliation in all posts, and we would all be very grateful if you would please adhere to this convention.

Regarding your question below, it seems like your WFs may not be entirely real. If you plot them (wannier_plot = true), the code should report at the end of the .wout file whether the WFs have any significant imaginary part.

Of course if you start the minimisation with an initial guess that is somewhat perverse (eg, with projection orbitals that have the wrong symmetry in comparison to what one expects to find) then the minimisation algorthim is going to have more difficulty in finding the correct WFs.

Best wishes,

Arash

—
Arash Mostofi — www.mostofigroup.org<http://www.mostofigroup.org>
Director, CDT in Theory and Simulation of Materials
Director, Thomas Young Centre @Imperial
Imperial College London

On 1 May 2017, at 15:59, balabi <balabi at qq.com<mailto:balabi at qq.com>> wrote:

I am new to wannier90 and after some experiences with it,  I found a problem.

I am using wannier90-2.1.0. Take example05 diamond as an example.

The example uses delicate initial projection

f=0.0,0.0,0.0:s
f=0.0,0.0,0.5:s
f=0.0,0.5,0.0:s
f=0.5,0.0,0.0:s

These are s orbitals located on center of C-C bond. I say the projection is delicate, because the spread is almost minimal even in the first iteration, so the convergence is fast. I use below convergence options

conv_window = 10
conv_tol = 1.d-15

the convergence is done in 74 steps. And examine hr.dat file, all imaginary part is zero.

   -3    1    1    1    1    0.007379    0.000000
   -3    1    1    2    1   -0.008540    0.000000
   -3    1    1    3    1   -0.008540    0.000000
   -3    1    1    4    1   -0.008540    0.000000
   -3    1    1    1    2   -0.008540   -0.000000


But as http://mailman.qe-forge.org/pipermail/wannier/2017-April/001350.html says for non-entangle case, wannierisation is robust to initial projection. As a test and for reproducibility, I choose below projection instead of random projection

f=0.0,0.0,0.0:dxy
f=0.0,0.0,0.5:dxy
f=0.0,0.5,0.0:dxy
f=0.5,0.0,0.0:dxy

conv_window and conv_tol are as previous. The convergence takes much more steps, totally 1168 steps. But the final state is the same to every digit in wout file, and xsf file visually the same in xcrysden

Final State
  WF centre and spread    1  ( -0.806995,  0.806995,  0.000000 )     0.58022874
  WF centre and spread    2  ( -0.000000,  0.000000, -0.000000 )     0.58022873
  WF centre and spread    3  ( -0.806995, -0.000000,  0.806995 )     0.58022875
  WF centre and spread    4  ( -0.000000,  0.806995,  0.806995 )     0.58022873
  Sum of centres and spreads ( -1.613990,  1.613990,  1.613990 )     2.32091495

         Spreads (Ang^2)       Omega I      =     1.954626519
        ================       Omega D      =     0.000000000
                               Omega OD     =     0.366288427
    Final Spread (Ang^2)       Omega Total  =     2.320914946

However, if we look at the hr.dat this time. The content is as below

   -3    1    1    1    1    0.007379    0.000000
   -3    1    1    2    1   -0.007476    0.004128
   -3    1    1    3    1    0.008130   -0.002616
   -3    1    1    4    1    0.008218   -0.002326
   -3    1    1    1    2   -0.007476   -0.004128
   -3    1    1    2    2    0.007379    0.000000
   -3    1    1    3    2    0.008382    0.001639

I really don't understand why such a significant imaginary parts considering that we have exactly the same wannierisation result？ Besides, I've tried many random projection all get same wannierisation, but failed to get even one clean hr.dat with zero imaginary part.
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