  The spin-half Heisenberg antiferromagnet (HAF) on the square and triangular
lattices is studied using the coupled cluster method (CCM) technique of quantum
many-body theory. The phase relations between different expansion coefficients
of the ground-state wave function in an Ising basis for the square lattice HAF
is exactly known via the Marshall-Peierls sign rule, although no equivalent
sign rule has yet been obtained for the triangular lattice HAF. Here the CCM is
used to give accurate estimates for the Ising-expansion coefficients for these
systems, and CCM results are noted to be fully consistent with the
Marshall-Peierls sign rule for the square lattice case. For the triangular
lattice HAF, a heuristic rule is presented which fits our CCM results for the
Ising-expansion coefficients of states which correspond to two-body excitations
with respect to the reference state. It is also seen that Ising-expansion
coefficients which describe localised, $m$-body excitations with respect to the
reference state are found to be highly converged, and from this result we infer
that the nodal surface of the triangular lattice HAF is being accurately
modeled. Using these results, we are able to make suggestions regarding
possible extensions of existing quantum Monte Carlo simulations for the
triangular lattice HAF.
