Using a combination of time-dependent density matrix renormalization group and single mode approximation, we investigate the dynamical structure factor of spin chains with antiferromagnetic nearest-neighbor $J_1$, next-nearest-neighbor $J_2$, and three-site $J_3$ interactions and show that, in all gapped phases and at the transitions between them, a simple physical picture can be obtained in terms of magnons and spin-1/2 domain-wall excitations or spinons. This applies to the fully dimerized phase, where a magnon mode clearly pops out of the two-spinon continuum for spin-1 and spin-3/2, and to the transition between the dimerized phase and the Haldane phase (resp. partially dimerized phase) for spin-1 (resp. spin-3/2), where spinons are deconfined along the transition but get confined across it when it is first order. Implications for the interpretation of inelastic neutron scattering in spin chains are briefly discussed.

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• Frustrated magnetism
• Magnetic phase transitions
• Magnetism
• Quasiparticles & collective excitations
• Spin dynamics
• Valence bond solid
• 1-dimensional spin chains
• Density matrix renormalization group