[Wannier] hidden actions taken by wannier90?

[Nicola Marzari]

Hi Jon,


(as usual, do sign your emails, so we know a bit more about you).

The problem is that the Wannier functions you obtain from minimization
of the spread can be invariant (mathematically, or just numerically)
with respect to certain unitary transformations - so the WFs do not
have the symmetry that you expect.

For this reason, we suggested in the 2002 PRB to perfrom an additional
transformation (that would not change the spread) that would remove this
degeneracy - for the case of d orbitals studied there is was the
diagonalization of <r^2>.

The choice of what you diagonalize depends on the symmetry you want to 
recover, and you might need to construct by hand (working on the code)
the additional matrix elements that are needed.

I never tried it, but if you were to give trial projections that
already had the riht symmetry, and the right shape, maybe the code
would not move away from that (even if there would be nothing
opposing it - so just numerical build-up could slowly shift you
away).

			nicola



jon wrote:
> Dear Prof. Marzari,
> 
> Let me see whether I interpret your paper right. Basically, for a 
> crystal with lower symmetry, MLWS could still have arbitrariness in 
> choosing its form. Thus, introducing a new criterion by minimizing <r^2> 
> could further reduce the arbitrariness, but not fully remove it. So, is 
> this what you mean by "to recover symmetries that are not built in in 
> the second-moment minimization"?
> 
> I guess the then relevant question related to my problem would be: is 
> minimization on <r^2> implemented in the wannier90 code? To help 
> understand the issue better, I would ask two more questions: is this 
> minimization equivalent to attempts to build in lattice symmetry 
> further, or in other words, is the removal of arbitrariness equivalent 
> in some sense to restoration of crystal symmetry for the wannier states? 
> Is there logic behind if this equivalence holds?
> 
> Thanks for your kind help,
> 
> Sincerely,
> Jon
> 
> On Thu, May 7, 2009 at 12:30 PM, Nicola Marzari <marzari at mit.edu 
> <mailto:marzari at mit.edu>> wrote:
> 
>     Nicola Marzari wrote:
> 
> 
> 
>         Dear Jon,
> 
> 
>         have a look at the Posternak...Marzari 2002 PRB. I presume that
>         that refers to your problem - you need to diagonalize in the
>         subspace of
>         localized orbitals to recover symmetries that are not built in in
>         the second-moment minimization.
> 
>         Let us know if that is the problem that affects you,
> 
>                    nicola
> 
> 
>         jon wrote:
> 
>             Dear Colleagues,
> 
>             I am working on DMFT applied to iron pnictide and need to
>             obtain the impurity Green function, which is basically the
>             bare Green function being summed over all the momentum
>             points in 1BZ. The tight-binding hoppings are extracted from
>             fitting to a band structure calculated through MLWS using
>             wannier90. These hoppings have cubic symmetry(on 2D plane
>             though). The impurity Green function turns out to be
>             diagonal in the orbital indices. This is not generally the
>             case unless the wannier states have been taken further
>             actions to form cubic harmonics(I am not an LDA expert, thus
>             please correct me if I am wrong here) before output.
>             However, the tutorial or introduction does not explicitly
>             mention this action and I am thus confused.
> 
>             Thanks,
> 
>             Sincerely,
>             Jon
> 
> 
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> 
> 
> 
> 
>     -- 
>     ---------------------------------------------------------------------
>     Prof Nicola Marzari   Department of Materials Science and Engineering
>     13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
>     tel 617.4522758 fax 2586534 marzari at mit.edu <mailto:marzari at mit.edu>
>     http://quasiamore.mit.edu
> 
> 


-- 
---------------------------------------------------------------------
Prof Nicola Marzari   Department of Materials Science and Engineering
13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu