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

Abstract

We investigate the magnetic excitations of the two-dimensional (2D) S = 1/2 trimerized Heisenberg models with intratrimer interaction J_1 and intertrimer interaction J_2 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=J_2/J_1 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.

Graphical abstract

Keywords

quantum Monte Carlo / trimerized Heisenberg model

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Declarations

The authors declare that they have no competing interests and there are no conflicts.

Acknowledgements

We would like to thank Anders W. Sandvik and Muwei Wu for the fruitful discussions. This project was supported by the NKRDPC-2022YFA1402802, NSFC-11804401, NSFC-11974432, NSFC-92165204, NSFC-12047562, NSFC-12122502, the Leading Talent Program of Guangdong Special Projects (No. 201626003), and Guangdong Basic and Applied Basic Research Foundation (No. 2023B1515120013). The calculations reported were performed on resources provided by the Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, No. 2022B1212010008. H. Q. W. also acknowledges the Youth S&T Talent Support Programme of Guangdong Provincial Association for Science and Technology (GDSTA) (No. SKXRC202404). J.Q.C. also acknowledges the financial support from the Special Project in Key Areas for Universities in Guangdong Province (No. 2023ZDZX3054) and the Dongguan Key Laboratory of Artificial Intelligence Design for Advanced Materials.

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