Emergent quasi-particles of spin-1 trimer chain

The recent experimental realization of emergent quasi-particles, such as spinons, doublons, and quartons, in a spin-$1/2$ trimer chain has spurred new interest in low dimensional magnetic systems. In this study, we investigate the dynamical properties of the isotropic spin-$1$ trimer chain with intra and inter-trimer antiferromagnetic exchange couplings, ($J >0$ and $J' >0$), respectively, unveiling various quasi-particles: magnons, singletons, triplons, pentons, and heptons. For weak inter-trimer exchange coupling $J'/J \ll 1$, it behaves as an effective spin-$1$ chain with valence bond solid (VBS) ground state. Employing density matrix renormalization group (DMRG) techniques, we compute the dynamic structure factor (DSF) which reveals a gapped magnon band alongside weakly dispersive singleton, excited triplon, and penton excitations. The evolution of these excitations with inter-trimer coupling $J'$ is also examined, providing insight into the underlying excitation mechanisms. For spin-$1$ chain, these exotic quasi-particles eventually reduce to conventional magnon excitations as $J'/J \rightarrow 1$. Our results shed light on the rich and complex excitation spectrum of spin-$1$ trimer chains and offer unique perspectives on the dynamics in quantum spin systems.