Fractional and composite excitations of antiferromagnetic quantum spin trimer chains

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.