[Wannier] Use of shifted ab initio k-grids

[Stepan Tsirkin]

Dear Wannier Experts,

I would like to raise a question, if it makes any sense to construct 
Wannier functions and perform Wannier interpolation starting from an ab 
initio grid that does not contain Gamma point. For example if the 
k-points along direction z  are kz=-1/2, kz=-1/6, kz=1/6  .  Such grids 
are frequently used in ab initio calculations, but all Wannier90 
examples include Gamma point. However I did not find a statement that 
such shifted grids are forbidden, neither in the literature not in the 
Wannier90 manual.

In my view the problem is that Wannier functions are considered periodic 
in the real-space (R-vectors) with the period equal to the size of the 
ab initio grid. In particular, the minimal-distance replica selection 
method (see sec 4.2 
https://iopscience.iop.org/article/10.1088/1361-648X/ab51ff/meta#cmab51ffs4 
) explicitly assumes

H(R+T) = H(R)

however, if one uses a shifted k-grid, it becomes

H(R+T) = - H(R)

So, many things may go wrong with such assumption.

Therefore my question - am I right? If so, should we  explicitly 
disallow the use of shifted grids, by stopping the calculation if Gamma 
point is not on the grid? Or at least show a warning, and mention this 
in the user manual? What is your opinion?

Or does someone of you regularly use shifted grids and that makes no 
practical problems?  What is your experience?

Best Regards,

Stepan Tsirkin,
University of Zurich.

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