N= CCM E$_{g}$/N CCM Gap 4 − 0.5 1 6 − 0.46712928 0.684740 8 − 0.45638668 0.522676 10 − 0.45154464 0.423239 12 − 0.44894924 0.355848 N= E$_{g}$/N Gap 2 − 1.263853992 1.4876903286 4 − 1.29781459 1.038539433 6 − 1.436237197 0.720627363 TABLE I: CCM LSUB m results for the ground-state energy and excitation energy gap of spin-half antiferromagnetic Heisenberg chains of N length with periodic boundary conditions. TABLE II: CCM SUB n - m results (with n = 2 N and m = N ) for the ground-state energy and excitation energy gap of spin-one antiferromagnetic Heisenberg chains of N length with periodic boundary conditions. was found to be very stable, as is generally also the case for extended systems ( N → ∞ ) in which the model state is known to be a “good starting point”. These results prove the principle that the CCM may be used to study finite-sized lattices. IV. CONCLUSIONS Again, we remark that recent developments of high-order CCM have been to extend existing formalism and codes to s ≥ 1 2 for both the ground and excited states [52], and independently to “generalised” expectation values for a wide range of one- and two-body spin operators [53]. We note that the CCM is that the Goldstone linked-cluster theorem is obeyed at all levels of approximation and so it provides results in the infinite lattice limit N → ∞ from the outset. In this article, we have shown the exact ground state for the 10