nearest-neighbour bonds lead to a competition in the quantum system. Henceforth, we choose an energy scale such that J = 1. The four-site plaquettes in the unit cell become de-coupled only in the limit J $^{′}$/J → 0. The ground state is a product of such four-site plaquette singlets in this limit. In the limit that J $^{′}$/J → ∞ dimers are formed on the J ′ bonds. To model such states using the CCM we start again from the N´ eel model state; namely, a state in which the spins on nearest-neighbour sites are anti-parallel. To create an exact plaquette-singlet product VBC ground state at J $^{′}$/J = 0 using the CCM we have to adjust the nearest-neighbour correlation coefficients S a 2 and S b 2 and a single four-body plaquette correlation coefficient S p 4 containing all four sites properly. (Note that S a 2 represents those ket-state coefficients for the nearest-neighbour two-body cluster connecting sites on a plaquette indicated by the solid lines in Fig. 1, whereas S b 2 represents those ket-state coefficients for the nearest-neighbour two-body cluster connecting sites on a dimer indicated by the dotted lines in the same figure. The coefficient S p 4 represents those ket-state coefficients for the four-body cluster corresponding to a plaquette indicated by the solid lines in Fig. 1.) Indeed, it is easy to show that setting the ket-state correlation coefficients S a 2 and S p 4 to a value of 0.5 and all other ket-state correlation coefficients (including S b $_{2}$) to zero the plaquette-singlet product valence-bond crystal state is obtained exactly. Furthermore, we are also able to reproduce exactly the dimer-singlet product ground state in the limit J $^{′}$/J → ∞ . In this limit, the nearest-neighbour ket-state correlation coefficient S b 2 on the dimer bonds (dotted lines in Fig. 1) has a value of one and all other coefficients (e.g., S a 2 and S p $_{4}$) are zero. An important point is that in the limits J $^{′}$/J → 0 and | J $^{′}$/J | → ∞ the system is comprised of independent clusters. However, the system is two-dimensional for all other values of J $^{′}$/J . This system therefore “interpolates” between a zero-dimensional and two- dimensional lattice with the bond strengths J $^{′}$/J . This model (and similar models) may therefore be used to study the differences between zero-dimensional and two-dimensional systems. They may also be used to investigate the effects of “linking” magnetic clusters in order to form an extended two-dimensional material. Such models are of interest in the subject of quantum computational. We remark that the CCM solution at intermediate values of J $^{′}$/J may be found by “tracking” the exact CCM solution by making small incremental changes in J $^{′}$/J from either of the exact limits J $^{′}$/J → 0 and | J $^{′}$/J | → ∞ (see Ref. [50] for details). 7