The ABINIT Users Mailing List ( CLOSED )

[Nicola Marzari <marzari@mit.edu>]

Alex Kutana > I am still trying to figure out how this phase 
indeterminacy of M_nn(k,b)
> affects other quantities depending on it, such as centers and spreads 
> of the Wannier functions, but this is another issue, not related 
> to my original question. 


Dear Alex,

the max-loc Wannier function recipe is indeed the attempt to
choose these arbitrary gauges (both the phase, and the unitary
mixings between different bands at the same kpoint) so that the
resulting u_nk's are as smooth as possible (smoothness in reciprocal
space translates in localization in real space). Note that
turning around 180 degrees (i.e. -1) for an infinitesimal change in
k-point is a discontinuity, and the resulting Wannier function
would be a mess (of course, if you have infinite k-points, and only
one is turned around, the mess does tend to zero). But the
"unphysical/unappealing" solutions one can get by minimizing
the localization functional often amount to having done a really
good job everywhere at setting these phases/rotations, but ending
up to a single point "topological" discontinuity (a little bit like
the old problem of combing a sphere, and you end up with one point
where you can't comb). Luckily, there is a solution here that
doesn't require going bald - that's what we do with our initially
guesses at the phases. By the way, all of this can be instructively
explored for one band in one dimension - the max-loc WFs there
have a constant phase between one key point and the other - basically
an identical fraction of the total Berry phase.

We can discuss all of this offline (perversely, I am tempted to
mention that outside the window a thai beach awaits).

Last - I believe there is an ongoing effort to link abinit with the
wannier code; maybe others can comment.


                        nic


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Prof Nicola Marzari   Department of Materials Science and Engineering
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