  Recently, as demonstrated by an antiferromagnetic spin-lattice application,
we have successfully extended the coupled-cluster method (CCM) to a variational
formalism in which two sets of distribution functions are introduced to
evaluate Hamiltonian expectation. We calculated these distribution functions by
employing an algebraic scheme. Here we present an alternative calculation based
on a diagrammatic technique. Similar to the method of correlated-basis
functionals (CBF), a generating functional is introduced and calculated by a
linked-cluster expansion in terms of diagrams which are categorized and
constructed according to a few simple rules and using correlation coefficients
and Pauli exclusion principle (or Pauli line) as basic elements. Infinite
resummations of diagrams can then be done in a straightforward manner. One such
resummation, which includes all so-called ring diagrams and ignores Pauli
exclusion principle, reproduces spin-wave theory (SWT). Approximations beyond
SWT are also given. Interestingly, one such approximation including all
so-called super-ring diagrams by a resummation of infinite Pauli lines in
additional to resummations of ring diagrams produces a convergent, precise
number for the order-parameter of the one-dimensional isotropic model, contrast
to the well-known divergence of SWT. We also discuss the direct relation
between our variational CCM and CBF and discuss a possible unification of the
two theories.
