consider a simple interaction Hamiltonian of spin-1 boson. Each boson has 3 spin states : @@m*F=1,0,-1@@. We now use @@a*{m*F}@@ (@@a*{m*F}^{\dagger}@@) as the annihilation (creation) operator for different @@m*F@@ states.

@@H=a*1^{\dagger}a*{-1}^{\dagger}a*0a*0+h.c.@@

Obviously, this Hamiltonian does not conserve @@a*{m*F}^{\dagger}a*{m*F}@@ separately, but instead it conserves total @@S*z=a*1^{\dagger}a*1-a*{-1}^{\dagger}a_{-1}@@.

Now I have a problem. When I define a site set file for spin-1 Bose-Hubbard model, I need to define a IQIndex object with (Index, QN) pair. Can I use @@a*{mF}^{\dagger}a*{mF}@@ as a quantum number for QN objects ? That is, I may define them to be

```
Index(nameint("state name",n),1,Site),QN({Np1,1},{Nz0,1},{Nm1,1}));
```

where Np1=@@a*{1}^{\dagger}a*1@@, Nz0=@@=a*0^{\dagger}a*0@@ and Nm1=@@a*{-1}^{\dagger}a*{-1}@@.

Thank you.