Excitations and dynamical structure factor of J₁-J₂ spin-3/2 and spin-5/2 Heisenberg spin chains

We study the dynamical structure factor of the frustrated spin-3/2 J₁-J₂ 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 J₂ ≈ 0.32J₁, while the spinons, viewed as domain walls between degenerate valence bond solid states, become incommensurate at J₂ ≈ 0.4J₁ beyond the Lifshitz point (J₂ ≈ 0.388J₁). 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.