[Wien] density matrix normalization - expectation spin value

[Martin Gmitra]

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]