[QE-users] Irreducible set of k-points

[Paolo Giannozzi]

Not sure I understand the problem: if k is a Bloch vector and G a 
reciprocal-lattice vector, k+G is equivalent to k. This property can be 
used to reduce the number of inequivalent k-points needed for the sum 
over the (irreducible) Brillouin Zone

Paolo

On 10/02/2025 14:13, Lukas Cvitkovich wrote:
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> 
> Dear QE users and developers,
> 
> I am currently trying to reproduce the construction of an irreducible k- 
> point set as done by QE.
> For this, I set "verbosity = high" to get the symmetry operations 
> printed in the output file.
> I start from a uniform k-point mesh. Then, using the same symmetry 
> operations as QE, I transform every k-point and fold it back in the 
> first Brillouin zone.
> If the resulting k-point falls on another k-point of the uniform grid, 
> it is NOT irreducible.
> In this manner, as also described by Blöchl et al (Phys. Rev. B *49*, 
> 16223, 1994) I find the set of irreducible kpoints.
> 
> My code agrees with QE for a simple structure (fcc crystal tested and 
> verified) but I have problems with a more complicated case (the 2D 
> magnet FGT).
> In this example, 6 symmetry operations are found (see attached QE-output 
> file).
> Starting from a 3x3x3 uniform grid, the irreducible set of kpoints - 
> according to QE - contains 7 points. However, I find 12 irreducible k- 
> points.
> 
> First, please note, that every point found by QE is also contained in my 
> set. But I find additional points which (according to QE) should be 
> related by some symmetry operation. By looking at the weights, I could 
> figure out which kpoints should belong together.
> For instance: According to QE, the kpoints [1/3, 0, 0] and [2/3, 0, 0] 
> are equivalent, as well as [0, 0, 1/3] and [0, 0, 2/3] should be 
> equivalent too. I recognized that all the extra points could be 
> transformed into each other by translating the lattice. However, 
> applying all the symmetry operations from the QE output file (these are 
> exclusively rotations and not translations), I cannot transform these 
> points into each other. You might try for yourself.
> 
> So the question that I would like to ask is: Are there any "hidden" 
> symmetry operations which are not explicitly printed in the output file? 
> Could fractional translations be the reason? Is it maybe related to 
> differences between point group and space group? Any other hints to what 
> I am missing?
> 
> Thank you! Your help would be highly appreciated!
> 
> Best,
> Lukas
> 
> 
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-- 
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 206, 33100 Udine Italy, +39-0432-558216