[QE-users] symmetry traces in sym_band.f90

[Gerson J. Ferreira]

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.

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 *, "======================================================"

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.

Best,
--
Gerson J. Ferreira
Prof. Dr. @ InFis - UFU
----------------------------------------------
gjferreira.wordpress.com
Institute of Physics
Federal University of Uberlândia, Brazil
----------------------------------------------


On Sun, Mar 6, 2022 at 10:35 PM Hongyi Zhao <hongyi.zhao at gmail.com> wrote:

> On Mon, Mar 7, 2022 at 2:39 AM Gerson J. Ferreira
> <gersonjferreira at ufu.br> wrote:
> >
> > Dear QE users,
> >
> > I need the matrix representation for the symmetry operators in the basis
> of the QE bands, so I'm checking how to edit the file sym_band.f90 for this
> purpose.
> >
> > The SUBROUTINE find_band_sym_so already calculates the trace as (loops
> are implied)
> >>
> >> trace(iclass,igroup)=trace(iclass,igroup) + DOT_PRODUCT
> (evc(:,ibnd),evcr(:,ibnd))
> >
> >
> > So, at first I imagined that a simple change would allow me to get the
> full matrices as (loops are implied)
> >>
> >> matrep(iclass,igroup,i,j) = DOT_PRODUCT (evc(:,ibnd),evcr(:,jbnd))
> >
> >
> > But I've noticed that the traces are "wrong". If I print as
> >>
> >> PRINT *, 'Class:', name_class_so(iclass)
> >> PRINT *, 'Trace:', trace(iclass,igroup)
> >
> > Both the trace and the matrices (matrep) above don't match the expected
> results. For instance, all double group bar-irreps are showing trace = 0.
> >
> > In the second part of this subroutine, where the code identifies the
> symmetry representations, I don't understand some of the IFs there, and the
> meaning of the variable "shift". So I guess I'm misreading something.
> >
> > Could someone help me understand what I am doing wrong?
>
> First, the method implemented in "./PP/src/sym_band.f90" is just a
> rough partial implementation, as indicated by the comment in the above
> source code file:
>
> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
> SUBROUTINE find_band_sym_so (ik,evc,et,nsym,s,ft,d_spin,gk, &
>      invs,rap_et,times,ngroup,istart,accuracy)
>
>   !
>   !   This subroutine finds the irreducible representations of the
>   !   double group which give the transformation properties of the
>   !   spinor wavefunctions evc.
>   !   Presently it does NOT work at zone border if the space group of
>   !   the crystal has fractionary translations (non-symmorphic space
> groups).
>   !
>   !
> !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
>
> 2. As an alternative, if I understand correctly, the following
> packages are currently available for this purpose, as discussed here
> [1]:
>
> A.  https://github.com/qeirreps/qeirreps
> B. https://github.com/stepan-tsirkin/irrep
>
> [1] https://github.com/goodluck1982/SpaceGroupIrep/issues/6
>
> Regards
> --
> Assoc. Prof. Hongsheng Zhao <hongyi.zhao at gmail.com>
> Theory and Simulation of Materials
> Hebei Vocational University of Technology and Engineering
> No. 473, Quannan West Street, Xindu District, Xingtai, Hebei province
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