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

The two-magnon problem in the k = − π/2 sector of a finite-size spin-1/2 chain with ferromagnetic nearest-neighbor (NN) interaction (J₁ > 0) and antiferromagnetic next-nearest-neighbor (NNN) interaction (J₂ < 0) and anisotropy parameters Δ₁ and Δ₂ 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 J₁/(∣J₂∣Δ₂)-Δ₁ 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 Δ₁ and Δ₂ are small (large) enough. Our results for the isotropic case Δ₁ = Δ₂ = 1 are consistent with an early work [Ono I, Mikado S and Oguchi T 1971 J. Phys. Soc. Japan 30 358].