Determination of Boundary Scattering, Intermagnon Scattering, and the Haldane Gap in Heisenberg Chains

Low-lying magnon dispersion in a S=1 Heisenberg antiferromagnetic (AF) chain is analyzed using the non-Abelian DMRG method. The scattering length $a_{\rm b}$ of the boundary coupling and the inter-magnon scattering length $a$ are determined. The scattering length $a_{\rm b}$ is found to exhibit a characteristic diverging behavior at the crossover point. In contrast, the Haldane gap $Δ$, 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 $Δ= 0.0891623(9)$ using a chain length longer than the correlation length $ξ$.

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