Accurate Results from Perturbation Theory for Strongly Frustrated S=1/2 Heisenberg Spin Clusters

We investigate the use of perturbation theory in finite sized frustrated spin systems by calculating the effect of quantum fluctuations on coherent states derived from the classical ground state. We first calculate the ground and first excited state wavefunctions as a function of applied field for a 12-site system and compare with the results of exact diagonalization. We then apply the technique to a 20-site system with the same three fold site coordination as the 12-site system. Frustration results in asymptotically convergent series for both systems which are summed with Pad\'e approximants. We find that at zero magnetic field the different connectivity of the two systems leads to a triplet first excited state in the 12-site system and a singlet first excited state in the 20-site system, while the ground state is a singlet for both. We also show how the analytic structure of the Pad\'e approximants at $|\lambda| \simeq 1$ evolves in the complex $\lambda$ plane at the values of the applied field where the ground state switches between spin sectors and how this is connected with the non-trivial dependence of the $<S^{z}>$ number on the strength of quantum fluctuations. We discuss the origin of this difference in the energy spectra and in the analytic structures. We also characterize the ground and first excited states according to the values of the various spin correlation functions.