[QE-users] symmetry traces in sym_band.f90

[Hongyi Zhao]

On Mon, Mar 7, 2022 at 10:00 AM Gerson J. Ferreira
<gersonjferreira at ufu.br> wrote:
>
> Thanks for the answer and the links. But if I understand correctly, these codes only give us the irreps, and I need the specific representation matrices calculated from the QE wave-functions. The best way to get these seem to be editing this routine.

Let us discuss this in more detail. An irreps is short for irreducible
representation [1], which is a component of a character table [2]: a
two-dimensional table whose rows correspond to irreducible
representations. The specific representation matrices calculated from
the QE wave-functions should also can be derived from the character
table.

So, I still don't quite understand what you mean above. Any more
hints/explanations/comments will be greatly appreciated.

[1] https://en.wikipedia.org/wiki/Irreducible_representation
[2] https://en.wikipedia.org/wiki/Character_table

> I've found my mistake, and a bug (I'll report for the developers as well). My mistake was that I was not using the "which_irr_so(iclass)" to identify the class. I was assuming that "iclass" would already list the classes in the correct order.
>
> Now, the bug is that "which_ir_so" is returning the class 9 two times here, but one of these should be 6 instead. This can be checked with the following code
>
> PRINT *, "======================================================"
> PRINT *, "which_ir_so:", (which_irr_so(iclass), iclass=1, nclass)
> PRINT *, "classes:", (name_class_so(iclass), iclass=1, nclass)
> DO irap=1,nrap
> PRINT *, ">>", (char_mat_so(irap, which_irr_so(iclass)), iclass=1, nclass)
> ENDDO
> PRINT *, "======================================================"

I want to know how you can make the above code display black
background color in this email.

> Which prints
>
> which_ir_so(iclass):           1           5           3           9           9           7           2           4           8
> classes: E    -E   2C3  -2C3  3C2' s_h 2S3  -2S3  3s_v
>
> So, the classes are ordered as {E, 3C2', 2C3, 3s_v, 3s_v, 2S3, -E, -2C3, -2S3}
>
> Notice that 3s_v appears twice, and s_h does not appear in the list.

What's your patched code? Could you please show the detailed steps to
reproduce the above example?

Best,
Hongyi