Determination of boundary scattering, magnon-magnon scattering, and the Haldane gap in Heisenberg spin chains

Low-lying magnon dispersion in a S = 1 Heisenberg antiferromagnetic (AF) chain is analyzed using the non-Abelian density-matrix-renormalization-group (DMRG) method. The scattering length a(b) of the boundary coupling and the intermagnon scattering length a are determined. The scattering length a(b) is found to exhibit a characteristic diverging behavior at the crossover point. In contrast, the Haldane gap Delta, the magnon velocity v, and a remain constant at the crossover. Our method allowed estimation of the gap of the S = 2 AF chain to be Delta = 0.0891623(9) using a chain length longer than the correlation length xi.