Interaction-round-a-face density-matrix renormalization-group method applied to rotational-invariant quantum spin chains

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 Sᵢ·Sᵢ₊₁ are explicitly derived. Using the IRF-DMRG with these IRF weights, the Haldane gaps Δ and the ground state energy densities e₀ for both $S=1$ and $S=2$ isotropic antiferromagnetic Heisenberg quantum spin chains are calculated by keeping up to only $m=90$ states.