Effective Hamiltonian for a Half-filled Hubbard Chain with Alternating   On-site Interactions
  We derive an effective spin Hamiltonian for the one-dimensional half-filled Alternating Hubbard model in the limit of strong on-site repulsion. We show that the effective Hamiltonian is a spin $S=1/2$ Heisenberg chain with asymmetric next-nearest-neighbor (nnn) exchange. 
Paata Kakashvili and George I. Japaridze