Haldane gap for theS=2antiferromagnetic Heisenberg chain revisited

Using the density matrix renormalization group (DMRG) technique, we carry out a large scale numerical calculation for the $S=2\mathrm{}$ antiferromagnetic Heisenberg chain. Performing systematic scaling analysis for both the chain length L and the number of optimal states kept in the iterations m, the Haldane gap $\Delta \mathrm{}\left(2\right)\mathrm{}$ is estimated accurately as $(0.0876\mathrm{}\pm 0.0013)J.$ Our systematic analysis for the $S=2\mathrm{}$ chains not only clarifies the controversies arising from various DMRG calculations and Monte Carlo simulations, but also sheds light on how to obtain reliable results from the DMRG calculations for other similar complicated systems.