[Q-e-developers] [Pw_forum] Test on the WF phase in QE

[Samuel Poncé]

Dear all,

I would like to present the following test:
1) Diamond with the normal 48 sym (incl frac translation)

VS

2) Diamond where the code is tricked into having two different type of atom
with two psp (24 sym & no frac translation). The two psp are the same with
a different name.

The input files are join to this email (first I do a scf calc followed by a
nscf calc where I put by hand all the kpoints).

The two case should in theory give exactly the same physical observable.

However, when I print the ground state WF summed on G-vectors and bands for
each k-points: SUM(evc(:,:)) where the evc dim are evc(npw,nbnd).
I get for the first case:
 ik            1
 SUM(evc) (0.524554603771020,-0.985842296616562)
 ik            2
 SUM(evc) (-0.210256090577016,0.545845252785036)
 ik            3
 SUM(evc) (-0.239028680198133,-1.83612435123587)
 ik            4
 SUM(evc) (-0.565218210001339,-0.820699742516653)
 ik            5
 SUM(evc) (1.42454745428565,-0.957929628317023)
 ik            6
 SUM(evc) (-0.274745448323905,1.09643888529245)
 ik            7
 SUM(evc) (-0.933074272062335,1.16077508535444)
 ik            8
 SUM(evc) (0.989923346231570,-1.58533060259471)
 ik            9
 SUM(evc) (-1.26782798392043,-0.150960156635521)
 ik           10
 SUM(evc) (-0.401891345164427,1.27585476000084)
.......
For the second case
 ik            1
 SUM(evc) (0.116807098229033,-1.11058471838606)
 ik            2
 SUM(evc) (-0.215236454279303,0.546415812538992)
 ik            3
 SUM(evc) (-0.239955952913802,-1.83623414069791)
 ik            4
 SUM(evc) (-0.566091061918831,-0.820097940655045)
 ik            5
 SUM(evc) (1.42304578433157,-0.960163474240552)
 ik            6
 SUM(evc) (-0.281026989151429,1.09416630115645)
 ik            7
 SUM(evc) (-0.933137702445232,1.16063633276210)
 ik            8
 SUM(evc) (0.989188453055074,-1.58571465239844)
 ik            9
 SUM(evc) (-1.26782806755424,-0.150960132814025)
 ik           10
 SUM(evc) (-0.401891332187340,1.27585476604143)

You can see that their norm is well the same but for some k-point the phase
is exactly the same whereas for other k-point the phase is strongly
different.
I must also add that the values that are different cannot be found at other
k-point in the other example. It is therefore not a problem of k-ordering.

This lead to a problem for me because I try to look at
<\Psi_k+q| might be something here or not |\psi_k>.

Therefore if the k are the same but the k+q point happen to have a phase
difference, such phase does not cancels out.

Is there a way to impose to have the same phase for the two case or a
maximum have a global phase that does not depend on the k-point?

Best Regards,

Samuel Ponce
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