[Wien] lapw5

[Peter Blaha]

Unfortunately, your statement:

 > Now, I have 2 degenerate eigenvalues at some energy, in my case e.g.
 > eigenvalue #1461 and #1462. In principle one of them should host spin-up
 > state on side A of the slab, and the other should host spin-dn state at
 > side B of the slab.

is wishful thinking.

For degenerate states, ANY linear combination of the degenerate states 
is a proper solutions and as far as I know, any diagonalizer will give 
you such an arbitrary linear combination. In addition, also the phases 
are completely arbitrary and cannot be influenced from "outside".

And you have found a particular linear combination, which "fulfils your 
expectations". This is all you can expect.

PS: Using different "numerics" (eg. different OMP parallelization, 
different compilation-optimizations, sequential vs. mpi diagonalizer, 
...) may lead to a different linear combination, but most likely none of 
them will fulfil your "expectations".


Am 27.05.2025 um 16:28 schrieb Lukasz Plucinski:
> It seems gmail did not send my last email, so I am trying again:
> 
> Dear All,
> 
> A bit more information on my lapw7 issue.
> 
> First of all, my degenerate states are not orthogonal. Perhaps their 
> linear combinations are.
> 
> I calculate charge density for a particular k and a particular state 
> number. I work with a symmetric slab of the 1T TMDC lattice. For a 
> surface state, this means that what is spin-up on side A of the slab 
> should be spin-dn on side B of the slab, |Psi_k_A(r)| = |Psi_k_B(-r)| 
> (sides A and B are symmetric, r=0 is e.g. in the middle of the slab).
> 
> Now, I have 2 degenerate eigenvalues at some energy, in my case e.g. 
> eigenvalue #1461 and #1462. In principle one of them should host spin-up 
> state on side A of the slab, and the other should host spin-dn state at 
> side B of the slab. However, this is not the case, and the charge of the 
> surface states is shared by the eigenvalues (this also makes the states 
> non-orthogonal).
> 
> lapw7 can calculate the full wave function with the phase. Now the 
> following DOES NOT hold:
> 
> NOT TRUE: |Psi_k_#1461_A_up(r) + Psi_k_#1462_A_up(r)| = | 
> Psi_k_#1461_B_up(-r) + Psi_k_#1462_B_up(-r)|
> 
> But the following holds:
> 
> TRUE: |Psi_k_#1461_A_up(r) + Psi_k_#1462_A_up(r)| = |Psi_k_#1461_B_up(- 
> r) - Psi_k_#1462_B_up(-r)|
> 
> This means that the spin-dn wave functions need to be added out-of-phase 
> to obtain what is expected. Actually, from the 2D plot of the phase of 
> Psi one can see that, for the two degenerate eigenvalues, spin-up wave 
> functions are in-phase, and spin-dn wave functions are out-of-phase.
> 
> Can you comment and advise how to deal with that?
> 
> Best,
> Lukasz
> 
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-- 
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Peter Blaha,  Inst. f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-158801165300
Email: peter.blaha at tuwien.ac.at
WWW:   http://www.imc.tuwien.ac.at      WIEN2k: http://www.wien2k.at
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