[Wannier] Req. uniqueness of Maximally localized Wannier functions

[Nicola Marzari]

Hi Soumyadeep,

plenty of literature on this, but some cases are discussed in Sec III of
https://arxiv.org/abs/1909.00433

In a nutshell: for non-magnetic insulators, the localization functional 
on the occupied bands seems to have one (or multiple, by symmetries - 
think benzene) well defined global minimum - all others correspond to 
messed-up phase factors, give rise to meaningless WFs, and those are not 
real (i.e. they have an imaginary components). I cannot discount though 
that e.g. during a mol. dyn. simulations one could find discontinuous 
jumps in the MLWFs centers from one timestep to another.

For non-magnetic systems where you disentangle also the empty bands, you 
can have more subtle, complex effects (see discussion above). In that 
respect, it also dependes if we call maximally localized the global 
minimum only, or also other local minima where WFs are real and look 
meaningful.

For magnetic system, we have less case studies, and in general there are 
already multiple local minima of the KS-DFT functional.

If anyone has experiences something different, welcome to mention it here.

				nicola


On 09/03/2020 06:21, Soumyadeep wrote:
> Dear All,
> 
>    I have a query, is Maximally localized Wannier functions are unique 
> set of functions? I mean for a particular system only one set of MLWF is 
> possible or it can be many set depending on other factors?
> 
>    Waiting eagerly for your reply.
> 
> with many thanks and best regards
> Soumyadeep
> -------------------------------------------------------------------
> Soumyadeep Ghosh,
> Senior Research Fellow,
> Homi Bhabha National Institute (HBNI),
> Raja Ramanna Centre for Advanced Technology, Indore, India-452013
> Mob: (+91)9424664553
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> Email: soumyadeepghosh35 at gmail.com, soumyadeep at rrcat.gov.in
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-- 
----------------------------------------------------------------------
Prof Nicola Marzari, Chair of Theory and Simulation of Materials, EPFL
Director, National Centre for Competence in Research NCCR MARVEL, EPFL
http://theossrv1.epfl.ch/Main/Contact http://nccr-marvel.ch/en/project