Derivation of the Hamiltonian of the Heisenberg model

1. Oct 21, 2007

genloz

1. The problem statement, all variables and given/known data
Show that the Hamiltonian of the Heisenberg model can be written as:
$$H=\sum^{N}_{k=1}[H_{z}(k)+H_{f}(k)]$$
where
$$H_{z}(k)\equivS^{z}(k)S^{z}(k+1)$$
$$H_{f}(k)\equiv(1/2)[S^{+}(k)S^{-}(k+1)+S^{-}(k)S^{+}(k+1)]$$

2. Relevant equations
As above

3. The attempt at a solution