Exact solution of the two-magnon problem in the $k=-\pi /2$ sector of a finite-size anisotropic spin-1/2 frustrated ferromagnetic chain

Abstract

The two-magnon problem in the $k=-\pi /2$ sector of a \emph{finite-size} spin-1/2 chain with ferromagnetic nearest-neighbor (NN) interaction $(J_1>0)$ and antiferromagnetic next-nearest-neighbor (NNN) interaction $(J_2<0)$ and anisotropy parameters ${\Delta }_1$ and ${\Delta }_2$ is solved exactly by combining a set of exact two-magnon Bloch states and a plane-wave ansatz. Two types of two-magnon bound states (BSs), i.e., the NN and NNN exchange BSs, are revealed. We establish a phase diagram in the $J_1/(|J_2|{\Delta }_2)$-${\Delta }_1$ plane where regions supporting different types of BSs are analytically identified. It is found that no BSs exist (the two types of BSs coexist) when both ${\Delta }_1$ and ${\Delta }_2$ are small (large) enough. Our results for the isotropic case ${\Delta }_1={\Delta }_2=1$ are consistent with an early work [Ono I, Mikado S and Oguchi T 1971 \emph{J. Phys. Soc. Japan} \textbf{30} 358].

10 pages, 5 figures, to appear in Physica Scripta

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