Exact solution of the two-magnon problem in the $k=-π/2$ sector of a finite-size anisotropic spin-1/2 frustrated ferromagnetic chain
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909805673709568 |
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| author | Li, Zimeng Wu, Ning |
| author_facet | Li, Zimeng Wu, Ning |
| contents | The two-magnon problem in the $k=-π/2$ 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 $Δ_1$ and $Δ_2$ 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 $J_1/(|J_2|Δ_2)$-$Δ_1$ 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 $Δ_1$ and $Δ_2$ are small (large) enough. Our results for the isotropic case $Δ_1=Δ_2=1$ are consistent with an early work [Ono I, Mikado S and Oguchi T 1971 \emph{J. Phys. Soc. Japan} \textbf{30} 358]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact solution of the two-magnon problem in the $k=-π/2$ sector of a finite-size anisotropic spin-1/2 frustrated ferromagnetic chain Li, Zimeng Wu, Ning Strongly Correlated Electrons The two-magnon problem in the $k=-π/2$ 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 $Δ_1$ and $Δ_2$ 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 $J_1/(|J_2|Δ_2)$-$Δ_1$ 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 $Δ_1$ and $Δ_2$ are small (large) enough. Our results for the isotropic case $Δ_1=Δ_2=1$ are consistent with an early work [Ono I, Mikado S and Oguchi T 1971 \emph{J. Phys. Soc. Japan} \textbf{30} 358]. |
| title | Exact solution of the two-magnon problem in the $k=-π/2$ sector of a finite-size anisotropic spin-1/2 frustrated ferromagnetic chain |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2509.09659 |