# [Wannier] Question about wannier center !

Jonathan Yates jry20 at cam.ac.uk
Wed Sep 17 17:23:50 CEST 2008

On Tue, 16 Sep 2008, lan haiping wrote:

>  I read several lines of wannier routines ,and try to understand several
> key
> points formulated in the paper and programme.
>  My question is about wannier center formulated in wannier90. In the MV
> paper,
> \bar{r}_n = -\frac{1}{N} \Sum_{k,b} w_b b Im lnM_{n,n}^{k,b}, while
> wan_omega
> subroutine formulates this equation with 2  quantities: sheet and csheet.
> I donot catch this point ,and donot know the meaning of this 2 quantities.
> Would you please explain some details in this  point ?

Unless you use the guiding centres option, csheet=1.0 and sheet=0.0 and
the formula in wann_omega reduces to the equation you reproduce above.

In the above formula (and that for Omega_D) there appears the log of
M_mn, ie the log of a complex number. This introduces a possible ambiguity
(ie different branch cuts - see section IV.D.2 of MV). In many cases this
causes no problems, but in certain systems it does cause problems in the
minimisation - typically one gets a few or many WF with very large spread,
and the value of Omega_D is large. One solution is to use the
guiding_centres option.
You will find more details in the wann_phases subroutine - here csheet
and sheet are computed. These are then used control the choice of branch
cut in wann_omega.

Jonathan

--
Dr Jonathan Yates         |    Theory of Condensed Matter Group
Corpus Christi College    |    Cavendish Laboratory
Cambridge, CB2 1RH, UK    |    Cambridge, CB3 OHE, UK
email jry20 at cam.ac.uk     |    Tel +44 (0)1223 337461