[Wien] density matrix normalization - expectation spin value

[Robert Laskowski]

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]
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> 



-- 
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