Towards Spin-Wave Like Approach to the J-J Heisenberg Antiferromagnet in Terms of Composite Spins

Conventional spin-wave approach relies on an expansion around a relevant classical (unentangled) ground state or equivalently the ground state in the mean field approximation for the quantum model. However, for systems which may admit valence bond ground states, such as the staggered J-J' Heisenberg antiferromagnet, single site mean field approximation is obviously an incorrect zeroth order approximation. In this paper, we introduce a mean field approximation for clusters consisting of two spins connected by a strong bond in the aforementioned model. We identify the quantum critical point and calculate the ground state magnetization within this cluster mean field approximation in one and two dimensions. Finally, we derive an effective dimer Hamiltonian, in the standard basis operator formalism, which may be a basis for further spin-wave like expansions around the cluster mean field approximation ground state.