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

TL;DR

This paper uses non-Abelian DMRG to analyze magnon dispersion in S=1 Heisenberg chains, determining scattering lengths, the Haldane gap, and their behaviors at a crossover point, providing precise gap estimates for S=2 chains.

Contribution

It introduces a method to accurately determine boundary and inter-magnon scattering lengths and the Haldane gap in Heisenberg chains, revealing their behaviors at the crossover point.

Findings

Boundary scattering length diverges at crossover

Haldane gap and magnon velocity remain constant at crossover

Estimated S=2 chain gap as 0.0891623(9)

Abstract

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 $\Delta$, 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 $\xi$.