An interaction-round-a-face density-matrix renormalization-group (IRF-DMRG) method is developed for higher integer spin chain models which are rotational invariant. The expressions of the IRF weights associated with the nearest-neighbor spin-$S$ interaction ${\mathbf{S}}_i\cdot {\mathbf{S}}_{i+1\mathrm{}}$ are explicitly derived. Using the IRF-DMRG with these IRF weights, the Haldane gaps $\Delta$ and the ground state energy densities $e_0$ for both $S=1\mathrm{}$ and $S=2\mathrm{}$ isotropic antiferromagnetic Heisenberg quantum spin chains are calculated by keeping up to only $m=90\mathrm{}$ states.

• Received 1 September 1999

DOI:https://doi.org/10.1103/PhysRevE.61.3199