  We investigate the magnetic excitations of the trimerized Heisenberg models
with intra-trimer interaction $J_1$ and inter-trimer interaction $J_2$ on four
different two-dimensional lattices using a combination of stochastic series
expansion quantum Monte Carlo (SSE QMC) and stochastic analytic continuation
methods (SAC), complemented by cluster perturbation theory (CPT). These models
exhibit quasi-particle-like excitations when $g=J_2/J_1$ is small,
characterized by low-energy magnons, intermediate-energy doublons, and
high-energy quartons. The low-energy magnons are associated with the magnetic
ground states. They can be described by the linear spin wave theory (LSWT) of
the effective block spin model and the original spin model. Doublons and
quartons emerge from the corresponding internal excitations of the trimers with
distinct energy levels, which can be effectively analyzed using perturbation
theory when the ratio of exchange interactions $g$ is small. In this small $g$
regime, we observe a clear separation between the magnon and higher-energy
spectra. However, as $g$ increases, these three spectra gradually merge into
the magnon modes or continua. Nevertheless, the LSWT fails to provide
quantitative descriptions of the higher-energy excitation bands due to
significant quantum fluctuations. Notably, in the Collinear II and trimerized
hexagon lattice, a broad continuum emerges above the single-magnon spectrum,
originating from the quasi-1D physics due to the dilute connections between
chains. Our numerical analysis of these 2D trimers yields valuable theoretical
predictions and explanations for the inelastic neutron scattering (INS) spectra
of 2D magnetic materials featuring trimerized lattices.
