Magnon, doublon and quarton excitations in 2D S=1/2 trimerized Heisenberg models

We investigate the magnetic excitations of the two-dimensional (2D) S = 1/2 trimerized Heisenberg models with intratrimer interaction J₁ and intertrimer interaction J₂ on four different 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 = J₂/J₁ is weak, 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 perturbative calculation when the ratio of exchange interactions g is weak. In this weak g regime, we observe a clear separation between the magnon and higher-energy spectra. As g increases, doublon and quarton gradually merge into the magnon modes or some continua. 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. In addition, we also compare our numerical results to the experimental RIXS spectrum and analyze the difference. 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.