Magnetization of theS=2antiferromagnetic Heisenberg chain near the critical magnetic field

Using the density-matrix renormalization-group (DMRG) technique, we carry out a large scale numerical calculation for the $S=2\mathrm{}$ antiferromagnetic Heisenberg (AFH) chain. We obtain the magnetization curve of $S=2\mathrm{}$ chain near the critical field. The corrections to the magnetization due to the magnon-magnon interaction are the same order for $S=2\mathrm{}$ and $S=1\mathrm{}$ chains. By comparing the experimental magnetization with our calculation, we find that the gap obtained experimentally is about $0.08J$ which is close to the accurate DMRG estimation for the $S=2\mathrm{}$ AFH chain. Numerical errors in our large scale calculation are also discussed.