  Motivated by recent advancements in theoretical and experimental studies on
the high-energy excitations, we theoretically explore the quantum phase
transition and composite dynamics of the antiferromagnetic trimer chains in a
magnetic field using the exact diagonalization, density matrix renormalization
group, time-dependent variational principle and cluster perturbation theory. We
measure the entanglement entropy to uncover the phase diagram, encompassing the
XY-I, $1/3$ magnetization plateau, XY-II and ferromagnetic phases. Both
critical XY-I and XY-II phases are both described by the conformal field theory
with the central charge $c \simeq 1$. By analyzing the dynamical structure
factor, we elucidate the distinct features of spin dynamics across different
phases. In the regime of weak intertrimer interaction, we identify the
intermediate-energy and high-energy modes in the XY-I and $1/3$ magnetization
plateau phases as the internal trimer excitations, corresponding to the
propagation of doublon and quarton, respectively. Notably, the application of a
magnetic field splits the high-energy spectra into two branches labeled as the
upper quarton and lower quarton. Furthermore, we also explore the spin dynamics
of a trimerized model closely related to the quantum magnet
\ce{Na_2Cu_3Ge_4O_12}, and discuss the possibility of the quarton Bose-Einstein
condensation. Our results can be verified in the inelastic neutron scattering
experiments and provide deep insights for exploring the high-energy exotic
excitations.
