Quantum disorder due to singlet formation: The Plaquette lattice

I study the order/disorder transition due to singlet formation in a quantum spin system by means of exact diagonalization. The systems is build by spin 1/2 on a two-dimensional square lattice with two different kinds of antiferromagnetic Heisenberg interactions. The interaction J(p) connects 4 nearest neighbor spins on a plaquette. The interaction J(n) connects the plaquettes with each other. If J(p) = J(n) the systems reduces to the simple square lattice case. If one of the interactions becomes sufficiently larger then the other the purely quantum effect of singlet formation drives the system into a disordered phase with only short range correlations in the plaquettes and a spin gap. I study the transition point by evaluating the spin gap and spin-spin correlations. I compare the results with previously calculated data from a non-linear a model approach, spin wave theory and series expansion calculations. I confirm a critical value of J(n) approximate to 0.6 for the quantum phase transition point. (C) 2002 Published by Elsevier Science B.V.