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 $a_{\mathrm{b}}$ of the boundary coupling and the intermagnon scattering length $a$ are determined. The scattering length $a_{\mathrm{b}}$ 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 $\Delta =0.0891623\left(9\right)$ using a chain length longer than the correlation length $\xi$. DOI: http://dx.doi.org/10.1103/PhysRevB.84.054446 ©2011 American Physical Society