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

Abstract

Low-lying magnon dispersion in a S=1 Heisenberg antiferromagnetic (AF) chain is analyzed using the non-Abelian DMRG method. The scattering length $a_{\mathrm{b}}$ of the boundary coupling and the inter-magnon 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 $\Delta =0.0891623(9)$ using a chain length longer than the correlation length $\xi$.

6 pages, 3 figures, 1 table, accepted in Phys. Rev. B

References in corpus (3)

• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Hyperbolic Deformation on Quantum Lattice Hamiltonians
• Scaling Relation for Excitation Energy Under Hyperbolic Deformation

Cited by in corpus (8)

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• Comparative density-matrix renormalization group study of symmetry-protected topological phases in spin-1 chain and Bose-Hubbard models
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• Haldane Gaps of Large-S Heisenberg Antiferromagnetic Chains and Asymptotic Behavior
• Precise estimation of the S = 2 Haldane gap by numerical diagonalization
• Comparison of encoding schemes for quantum computing of $S>1/2$ spin chains
• Instability of the Haldane Phase: Roles of Charge Fluctuations and Hund's Coupling