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

TL;DR

This study explores magnetic excitations in 2D trimerized Heisenberg models, identifying magnon, doublon, and quarton quasiparticles, and analyzes their behavior across different interaction regimes using advanced numerical methods.

Contribution

It combines SSE QMC, SAC, and CPT to analyze trimerized 2D Heisenberg models, revealing distinct quasiparticle excitations and their evolution with interaction strength.

Findings

Magnon, doublon, and quarton excitations identified

Clear separation of spectra at small interaction ratios

Broad continuum observed in specific lattice geometries

Abstract

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.