# Effective Hamiltonian in Heisenberg model

How can we divide the whole matrix into submatrices that we can write effective Hamiltonian on the Heisenberg model Based on Fundamentals of the Physics of Solids book (Volume I) written by Jen˝o Sólyom, in chapter 14, page 464, (14.2.5) equation?

$$H_{eff} = E_s + (1/2) (E_t - E_s ) S_{total} ^2$$

$$S_{total} = S_1 + S_2$$