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A new approximation hierarchy, called the LPSUB$m$ scheme, is described forthe coupled cluster method (CCM). It is applicable to systems defined on aregular spatial lattice. We then apply it to two well-studied prototypical(spin-1/2 Heisenberg antiferromagnetic) spin-lattice models, namely: the XXZand the XY models on the square lattice in two dimensions. Results are obtainedin each case for the ground-state energy, the ground-state sublatticemagnetization and the quantum critical point. They are all in good agreementwith those from such alternative methods as spin-wave theory, seriesexpansions, quantum Monte Carlo methods and the CCM using the alternativeLSUB$m$ and DSUB$m$ schemes. Each of the three CCM schemes (LSUB$m$, DSUB$m$and LPSUB$m$) for use with systems defined on a regular spatial lattice isshown to have its own advantages in particular applications.

The Coupled Cluster Method Applied to Quantum Magnets: A New LPSUB$m$ Approximation Scheme for Lattice Models