Dear all,

Thanks Bo-Nan for useful comments.

Still, having corrected matrix element of S+ and S-, the results of measurements S^2 operator in two different ways, i.e. pm and mp,

<SITEOPERATOR name="pm" site="x"> Splus(x)*Sminus(x)+Sz(x)*Sz(x)-Sz(x) </SITEOPERATOR>

<SITEOPERATOR name="mp" site="x"> Sminus(x)*Splus(x)+Sz(x)*Sz(x)+Sz(x) </SITEOPERATOR>

are different. What is interesting, that when I change the definition,

<SITEOPERATOR name="pm" site="x"> Splus(x)*Sminus(x)+Sz(x)*Sz(x)+Sz(x) </SITEOPERATOR>

<SITEOPERATOR name="mp" site="x"> Sminus(x)*Splus(x)+Sz(x)*Sz(x)-Sz(x) </SITEOPERATOR>

the results are the same, as it should be. It is strange because the definitions of S+ and S- seems to be correct (after replacing matrix element from 1/2 to 1).

Volodymyr Derzhko

Thanks for catching this. Nobody has used these operators ever so far. S+ and S- for spin-1/2 of course have matrix element 1.

On Mar 6, 2013, at 1:03 AM, Bo-Nan JIANG <bonanjiang@gmail.com mailto:bonanjiang@gmail.com> wrote:

...

Hi, Matthias and ALPS people

I recheck the spin operator for fermion on wiki (where the matrix elements of Splus and Sminus are both given )http://en.wikipedia.org/wiki/Anti-symmetric_operator, but it seems the matrix elements of Splus and Sminus in SITEBASIS "fermion" and "alternative fermion" shall be one. I do not mean to be offensive. Trust me, this problem has already driven myself crazy. Maybe it is my mistake, so can you ALPS people be so kind to tell me where I am wrong or your special consideration when you define the above two matrix elements?

Bo-Nan

2013/3/5 Bo-Nan JIANG <bonanjiang@gmail.com mailto:bonanjiang@gmail.com>

Hi,all
we all know, for the angular momentum, the operator matrix
element of Jplus is sqrt(J*(J+1)-Jz(Jz+1)) and for Jminus, it is
sqrt(J*(J+1)-Jz(Jz-1)). Just as ALPS defines in SITEBASIS "spin".
So, it is straightforward that the spin-1/2 fermion with S=1/2,
the matrix elements of Splus and Sminus shall be
sqrt((1/2)*(1/2+1)-(-1/2)(-1/2+1))=1 and
sqrt((1/2)*(1/2+1)-1/2(1/2-1))=1 respectively. If I am right,
then why you guys define the matrix element of Splus and Sminus
in SITEBASIS "fermion" and "alternative fermion" all equal to 1/2?

Bo-Nan


-- 
Stay foolish,Stay hungry.

-- Stay foolish,Stay hungry.