# [Wannier] Negative spread for YBCO

Nicola Marzari marzari at MIT.EDU
Tue Jul 7 19:04:45 CEST 2009

```Jonathan Yates wrote:
>  If that isn't the cause of your problem, then I suspect the next step is to put
> the mmn,amn and eig files on a webserver - so that we can look at the problem in
> more detail. Unless anyone else has seen, and cured, this type of problem before?

Hi Simon, Jonathan -

indeed, it's a phase problem, and I'm pretty sure I've seen it
happen (12 years ago, so my memory might be hazy). The code uses
definitions 31 and 32 from the 97 PRB to calculate the spread,
but errors in phases do not cancel out when you subtract
the square of 31 from 32 .

What is an error in phase ? Well, let's take the simple example
of a very localized wannier function centered somewhere in r0.
If you use the equation in between 5 and 6, you'll see that M_nn^k,b
is a constant ndependent of k: exp (-i b.r0) (from which
Im ln M_nn^k,b gives you - b.r0, and eq 31 gives you r0 as the
center).

Now, suppose you are trying to get the WFs, and these are
getting localized, but not perfectly, and the M_nn^k,b is not perfectly
constant, and is such that for a vectot b in one direction it is just
above the branch cut, and for b in the opposite direction it is just
below the branch cut, then the sum of the two terms will be mismatched
(there is a 2pi between the two of them), and instead of averaging to
around r0, it averages to (r0+r0+lattice vector)/2, so it's really in
the middle. That's why it is important to choose phase factors so that
these problems do not arise, and that's what the sheet try to do in the
code - picking up a good estimate of the center to guess the most
appopriate phase factor.

In all of this, the golden rule is to start from carefully
chosen projections at the beginning - these usually solve all
problems.

nicola

---------------------------------------------------------------------
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

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