AI 中文总结
本文针对铁磁-反铁磁$J_1-J_2$正方格子模型，分析磁振子束缚态的异同、机制与演化，提出分波命名法和确定相边界的方法，为磁振子配对研究提供清晰框架。
AI 中文摘要
本文对海森堡$S=1/2$正方格子$J_1-J_2$铁磁-反铁磁模型中磁振子的配对与束缚态开展了全面分析，重点对比了格子上自旋翻转的束缚态与连续介质中粒子束缚态的异同。研究在整个布里渊区范围内分析了有限对动量下的磁振子束缚态，并倡导采用一种便捷的格子分波命名法；识别并量化了高对称对动量下束缚态稳定性增强或脆弱性的机制，分别对应有效维度的降低或提升。研究还表明这些效应可控制束缚态随模型参数的演化，为理解更一般场景下的磁振子配对提供了清晰框架，同时提出了一种确定束缚态相边界的方法。
英文摘要
A comprehensive analysis of pairing and bound states of magnons in the Heisenberg $S\!=\!1/2$ square-lattice $J_1\!-\!J_2$ ferro-antiferromagnetic model is presented. We highlight the similarities and differences between the bound states of spin flips on a lattice and those of particles in the continuum. Magnon bound states at finite pair momentum are studied throughout the Brillouin zone and a convenient lattice partial-wave nomenclature is advocated. The mechanisms of enhanced stability or fragility of these bound states for the high-symmetry pair momenta are identified and quantified as relating to the effective dimensional reduction or enhancement, respectively. These effects are also shown to control the evolution of the bound states with the model parameters, providing a transparent framework for understanding magnon pairing in a more general setting. A method to determine the bound state phase boundaries is presented.
Comments37 pages, 17 figures. Supplementary Material (SM) available under "Ancillary files"
