[Wien] density matrix normalization - expectation spin value

[Robert Laskowski]

After lapwso, vectors are non-pure spinors, it means they have both spin-up and spin-dn
parts non-zero. lapwso generates upso and dnso vectors that contains those parts, the energy files
upso and dnso are the same and they are contain all eigenvalues. If you would run lapwso but turning
off all atoms those files should contain eigenvalues from both energyup and energydn files.
So the <up|up> part of the spin matrix comes from integrating up and up part of the vector, 
<dn|dn> from dn part, for <up|dn> part you have to integrate the up part of the vector with dn part of the vector.

I think that you can use WIENNCM (non-collinear version of wien2k). There lapw2 generates full spin density matrix.
SO you would need to run it on a single k-point in a narrow energy window that selects your eigenvalue (ALL option, or 
hack lapw1 such that it outputs only one eigenvalue). lapw2 then prints magnetic moments ( grep for :ncmmm)
as vectors inside spheres (shere coordinate frame)  and in interstitial (cartesian), mixer rotates them into 
the same frame and prints total vector. If you have spin moment as vector,  you can easily generate spin density matrix

<up|up>=(n + mz)/2
 <dn|dn>=(n - mz)/2
<up|dn>=(mx + i*my)/2
<dn|up>=(mx - i*my)/2

regards

Robert

On Friday 05 February 2010 11:12:27 Martin Gmitra wrote:
> Hi Robert,
> 
> Actually we are interested in SOC case. Could you please provide some
> further hints how to get the off-diagonal part for spin density matrix?
> 
> Martin
> 
> 
> 
> On Fri, Feb 5, 2010 at 9:47 AM, Robert Laskowski <
> rolask at theochem.tuwien.ac.at> wrote:
> 
> > Yes, lapw2 calculates also interstitial charge density (fourir.F). You can
> > try to hack this, and add a routine that integrates
> > the charge density in interstitia, there should be one in mixer source.
> > Then interface it with your modified version of lapwdm.
> >
> > lapw2 does not calculate the off diagonal part of the spin density matrix,
> > which is non zero if SOC is present.
> > If you are not interested  in SOC, then easiest would be to use filtvec
> > program that filters vectors, strip it from  all
> > states except the one you are interested in and run lapw2 and mixer to get
> > the charge in interstitial.
> >
> >
> > regards
> >
> > On Thursday 04 February 2010 20:16:29 Martin Gmitra wrote:
> > > Hi Robert,
> > > Is there a way to include this somehow?
> > > Thanks,
> > > Martin
> > >
> > >
> > > On Thu, Feb 4, 2010 at 9:44 AM, Robert Laskowski <
> > > rolask at theochem.tuwien.ac.at> wrote:
> > >
> > > > Hi,
> > > > you are missing interstitial contribution.
> > > >
> > > > regards
> > > >
> > > > On Thursday 04 February 2010 09:36:53 Martin Gmitra wrote:
> > > > > Dear Wien2k users,
> > > > >
> > > > > We are interested in calculation of expectation value of spin for a
> > state
> > > > |n,k>,
> > > > > where n is the band index and k is the wave vector. For this purpose
> > we
> > > > have
> > > > > slightly modified lapwdm program. The problem we are encountering is
> > that
> > > > the
> > > > > expectation value of z-component of Pauli matrix (sigma_z) is not
> > equal
> > > > one.
> > > > > Let us assume for simplicity spin-up state |n,k> and no spin-orbit
> > > > coupling.
> > > > > The expectation value for sigma_z we calculate as
> > > > >
> > > > > sum_a ( rho_{n,k,a} sigma_z ) not= 1  (it is smaller then 1, typical
> > > > > range 0.6-0.9)
> > > > >
> > > > > where sum_a is the summation over atoms in unit cell.
> > > > >
> > > > > 1. Why we do not obtain for the state |n,k> expectation value equal
> > one?
> > > > > It is rather obvious that in this example <n,k| sigma_z |n,k> =1.
> > > > >
> > > > > 2. What is the density matrix normalization in this case?
> > > > >
> > > > > rho_{n,k,a} is in this simple example 2x2 matrix having only up-up
> > > > component,
> > > > > which is given as Trace in orbital subspaces (sum for L=0,1,2,3) of
> > given
> > > > state
> > > > > |n,k>.
> > > > >
> > > > > Many thanks in advance,
> > > > > Martin
> > > > >
> > > > > [We are running Wien2k v9.1]
> > > > > _______________________________________________
> > > > > Wien mailing list
> > > > > Wien at zeus.theochem.tuwien.ac.at
> > > > > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
> > > > >
> > > > >
> > > >
> > > >
> > > >
> > > > --
> > > > Dr Robert Laskowski
> > > >
> > > > Vienna University of Technology,
> > > > Institute of Materials Chemistry,
> > > > Getreidemarkt 9/165-TC, A-1060 Vienna
> > > >
> > > > tel. +43 1 58801 15675
> > > > Fax  +43 1 58801 15698
> > > > _______________________________________________
> > > > Wien mailing list
> > > > Wien at zeus.theochem.tuwien.ac.at
> > > > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
> > > >
> > >
> >
> >
> >
> > --
> > Dr Robert Laskowski
> >
> > Vienna University of Technology,
> > Institute of Materials Chemistry,
> > Getreidemarkt 9/165-TC, A-1060 Vienna
> >
> > tel. +43 1 58801 15675
> > Fax  +43 1 58801 15698
> > _______________________________________________
> > Wien mailing list
> > Wien at zeus.theochem.tuwien.ac.at
> > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
> >
> 



-- 
Dr Robert Laskowski

Vienna University of Technology, 
Institute of Materials Chemistry, 
Getreidemarkt 9/165-TC, A-1060 Vienna

tel. +43 1 58801 15675
Fax  +43 1 58801 15698