We study the dynamical structure factor of the frustrated spin-$3/2J_1\text{−}{J}_2$ Heisenberg chains, with particular focus on the partially dimerized phase that emerges between two Kosterlitz-Thouless transitions. Using a valence bond solid Ansatz corroborated by density-matrix renormalization-group simulations, we investigate the nature of magnon and spinon excitations through the single-mode approximation. We show that the magnon develops an incommensurate dispersion at $J_2\approx 0.32J_1$, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at $J_2\approx 0.4J_1$ beyond the Lifshitz point $(J_2\approx 0.388J_1)$. The dynamical structure factor exhibits rich spectral features shaped by the interplay between these excitations, with magnons appearing as resonances embedded in the spinon continuum. The spinon gap shows a nonmonotonic behavior, reaching a peak near the center of the partially dimerized phase and closing at the boundaries, suggesting the appearance of a floating phase as a result of the condensation of incommensurate spinons. Comparative analysis with the spin-$5/2$ case confirms the universality of these phenomena across half-integer higher-spin systems. Our results provide detailed insight into how fractionalization and incommensurate condensation govern the spectral properties of frustrated spin chains, offering a unified picture across different spin magnitudes.

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• Fractionalization
• Magnetism
• Quasiparticles & collective excitations
• Spin dynamics
• 1-dimensional spin chains
• 1-dimensional systems
• Density matrix methods
• Tensor network methods
• Tight-binding model