[QE-users] symmetry traces in sym_band.f90

[Hongyi Zhao]

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