[Wien] Meaning of density matrices for -so -orb

[Peter Blaha]

Spin-orbit couples spin-up and dn wavefunctions via l.s

Both, GGA+U or EECE enter the calculations via an effective (orbital
depended) potential (Vorbup/dn and the corresponding matrix elements in
the Hamiltonian read (in case of applications to d-electrons)

<psi(l=2)_up|Vorbup|psi'(l=2)_up>   and the same for dn.

This is done in both, in lapw1 and in lapwso. In the latter there is
in principle also a spin-coupling term  Vorbud , which couples up and dn
spin electrons, but this is switched off by default.

While for a case without inversion symmetry, there should not be any difference
whether one applies Vorb in lapw1 or lapwso, in a case with inversion symmetry
there is a BIG difference.
Vorb can be complex (in particular with spin-orbit and a magnetic case, where
it amplifies the orbital moment, i.e. the difference between the +m and -m components)
and when you apply the complex Vorb in lapw1 with a real Hamiltonian, you simply
throw away the imaginary parts of these matrix elements.

The definition of the density matrix does not change with/without SO, except that
without SO you have Dmatup=<psi_up|Psi_up>(l=2) and the same for the Psi-dn,
while with SO each psi_nk had a Psi_up AND dn component, so you must project out
the Dmatup from all states.


Am 23.05.2015 um 18:27 schrieb Laurence Marks:
> I am trying to understand exactly what spin-oribit & U (or eece) is doing, so a very simple question which does not appear to be cleanly spelt out in the user guide. When
> spin-orbit is included does the definition of the density matrices change to represent the presence of the mixed states?
>
> --
> Professor Laurence Marks
> Department of Materials Science and Engineering
> Northwestern University
> www.numis.northwestern.edu <http://www.numis.northwestern.edu>
> Corrosion in 4D: MURI4D.numis.northwestern.edu <http://MURI4D.numis.northwestern.edu>
> Co-Editor, Acta Cryst A
> "Research is to see what everybody else has seen, and to think what nobody else has thought"
> Albert Szent-Gyorgi
>
>
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-- 
-----------------------------------------
Peter Blaha
Inst. Materials Chemistry, TU Vienna
Getreidemarkt 9, A-1060 Vienna, Austria
Tel: +43-1-5880115671
Fax: +43-1-5880115698
email: pblaha at theochem.tuwien.ac.at
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