Coupled Cluster Treatment of the XY model

Abstract

We study quantum spin systems in the 1D, 2D square and 3D cubic lattices with nearest-neighbour XY exchange. We use the coupled-cluster method (CCM) to calculate the ground-state energy, the T=0 sublattice magnetisation and the excited state energies, all as functions of the anisotropy parameter $\gamma$. We consider $S=1/2$ in detail and give some results for higher $S$. In 1D these results are compared with the exact $S=1/2$ results and in 2D with Monte-Carlo and series expansions. We obtain critical points close to the expected value $\gamma=0$ and our extrapolated LSUBn results for the ground-state energy are well converged for all $\gamma$ except very close to the critical point.