[Wannier] Accuracy of fermi surface plot

[Jonathan Yates]

On Wed, 2 May 2007, Brad Malone wrote:

> Hi, I was wondering how accurate the eigenvalues given in the .BXSF file
> when outputting the fermi surface are.  Does increasing the number  of
> iterations (num_iter) increase the accuracy, or does this number only affect
> the Wannierization?

Brad,

  num_iter sets the maximum number of steps to take when minimising the 
spread of the Wannier functions. If you set this to a small number you may 
find that the spread of the WF is converged to only, say, 1x10-6 Ang^2, 
rather than machine precision.

  However, this should have no significant effect on the quality of the 
interpolated eigenvalues.[*] The Wannier interpolation procedure requires 
having well localised WF, rather than maximally localised WF (ie it 
doesn't matter if you're not at the exact minimum of the spread).

  The quality of the interpolated eigenvalues is determined by the spacing 
of the ab-initio k-point mesh used to compute the WF. In fact the quality 
of the interpolation increases exponentially with the spacing of this 
mesh.(denser k-grid => better interpolation). See cond-mat/0702554 
particularly the Appendix (this will appear in PRB shortly)

  In order for you to assess the quality of the interpolation I suggest the 
following procedure:

  Plot a band structure along various high symmetry directions using 
Wannier90.
  Plot an equivalent band-structure using your ab-initio code. Note: if 
you're using pwscf, Wannier90 will write a file <seedname>_band.kpt, which 
contains the path kpoints in pwscf format.
  Compare the two band-structures.
  Increase the density of the k-point mesh used to compute the WF until the 
interpolated bands have an accuracy sufficient for your needs.

  Yours
    Jonathan


[*] Of course this is a simple thing to check out numerically - so you 
don't have to take my word for it.

-- 
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