Using Lanczos exact diagonalization, stochastic analytic continuation of quantum Monte Carlo data, and perturbation theory, we investigate the dynamic spin structure factor $mathcal{S}(q,omega)$ of the $S=1/2$ antiferromagnetic Heisenberg trimer chain. We systematically study the evolution of the spectrum by varying the ratio $g=J_2/J_1$ of the intertrimer and intratrimer coupling strengths and interpret the observed features using analytical and numerical calculations with the trimer eigenstates. The doublet ground states of the trimers form effective interacting $S=1/2$ degrees of freedom described by a Heisenberg chain with coupling $J_{rm eff}=(4/9)J_2$. Therefore, the conventional two-spinon continuum of width $propto J_1$ when $g=1$ evolves into to a similar continuum of width $propto J_2$ in the reduced Brillouin zone when $gto 0$. The high-energy modes (at $omega propto J_1$) for $g alt 0.5$ can be understood as weakly dispersing propagating internal trimer excitations (which we term doublons and quartons), and these fractionalize with increasing $g$ to form the conventional spinon continuum when $g to 1$. The coexistence of two kinds of emergent spinon branches for intermediate values of $g$ give rise to interesting spectral signatures, especially at $g approx 0.7$ where the gap between the low-energy spinon branch and the high energy band of mixed doublons, quartons, and spinons closes. These features should be observable in inelastic neutron scattering experiments if a quasi-one-dimensional quantum magnet with the linear trimer structure and $J_2 < J_1$ can be identified. We suggest that finding such materials would be useful, enabling detailed studies of coexisting exotic excitations and their interplay within a relatively simple theoretical framework.
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