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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.

Background: Cerebrotendinous xanthomatosis is an autosomal recessive disorder of lipid metabolism caused by the mutation of the CYP27A1 gene encoding sterol 27-hydroxylase, an essential enzyme for the conversion of cholesterol to chenodeoxycholic and cholic acids. Cerebrotendinous xanthomatosis is a rare neurological disease with a wide range of clinical symptoms that are easily misdiagnosed., Case Summary: Here we report the clinical, biochemical, and molecular characterization of a 33-year-old female patient with cerebrotendinous xanthomatosis. The patient developed ataxia and had the typical symptoms of juvenile cataracts, tendon xanthomata, and progressive nervous system dysfunction. Magnetic resonance imaging of the brain revealed bilateral dentate nucleus lesions and white matter abnormalities. This patient was misdiagnosed for 2 years resulting in severe neurological complications. After 2 years of chenodeoxycholic acid treatment, she still presented with ataxia and dysarthria. The pathogenic sites of CYP27A1 were identified as c.255+1G>T and c.1263+1G>T, which were both caused by shear denaturation., Conclusion: Cerebrotendinous xanthomatosis requires a multidisciplinary diagnosis that must be made early to avoid progressive neurological degeneration. c.1263+1G>T is a known mutation, but c.255+1G>T is a rare mutation site., Competing Interests: Conflict-of-interest statement: All authors report no relevant conflicts of interest for this article., (©The Author(s) 2022. Published by Baishideng Publishing Group Inc. All rights reserved.)