  A new approximation hierarchy, called the LPSUB$m$ scheme, is described for
the coupled cluster method (CCM). It is applicable to systems defined on a
regular spatial lattice. We then apply it to two well-studied prototypical
(spin-1/2 Heisenberg antiferromagnetic) spin-lattice models, namely: the XXZ
and the XY models on the square lattice in two dimensions. Results are obtained
in each case for the ground-state energy, the ground-state sublattice
magnetization and the quantum critical point. They are all in good agreement
with those from such alternative methods as spin-wave theory, series
expansions, quantum Monte Carlo methods and the CCM using the alternative
LSUB$m$ 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 is
shown to have its own advantages in particular applications.
