Perturbation theory for the ground singlet state of the Heisenberg spin 1/2 antiferromagnetic chain

The Heisenberg spin 1/2 antiferromagnetic chain is considered. We use the perturbation theory where a collection of noninteracting clusters (chains with a small number of spins) is regarded as an unperturbed system and the interaction between clusters is regarded as a perturbation. The advantage of the perturbation theory is that it results in the proper thermodynamic limit. Expressions for corrections to the energy of the ground state of the chain are obtained up to the fourth order inclusive. The numerical results calculated for the infinite chain with the help of clusters containing 2, 4, 6, or 8 spins show good agreement with the exact value known from the Bethe ansatz. Bibliography: 9 titles.