The Hilbert space for the single site is H with the base { | S , S z ⟩ ⟩ } ≡ ≡ { | 1 , 1 ⟩ ⟩ , | 1 , 0 ⟩ ⟩ , | 1 , − − 1 ⟩ ⟩ } . With this base the spin operators are S x , S y and S z for the single site. For every block, the two blocks and the two sites, there is its own Hilbert space H b , its base { | w i ⟩ ⟩ } ( i : 1 … … dim ⁡ ⁡ ( H b ) )and its own operators O b : H b → → H b where