带可优化玻色截断的广义Holstein-Primakoff变换
Generalized Holstein-Primakoff transformation with optimizable bosonic truncation
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中文总结 AI 辅助
本文提出带可优化玻色截断的广义Holstein-Primakoff变换，将其应用于正方晶格自旋-1双线性-双二次模型，所得激发谱与张量网络结果高度吻合，可降低截断误差。
中文摘要 AI 辅助
自旋波理论为量子自旋系统的激发谱提供了准粒子描述，该理论中自旋算符通常通过Holstein-Primakoff变换或Dyson-Maleev变换进行玻色化。实际计算中，玻色化哈密顿量必须被截断，因此得到的激发谱依赖于玻色表示的选择。本文引入一种广义Holstein-Primakoff变换，它通过单一参数在传统Holstein-Primakoff变换与Dyson-Maleev变换之间连续插值，该形式自然扩展到SU(N)代数，为优化超越谐波阶的玻色截断提供了灵活框架。作为应用，研究了正方晶格上的自旋-1双线性-双二次模型，将广义Holstein-Primakoff变换与连续相似变换结合，得到的激发谱与张量网络计算结果高度吻合，表明优化玻色表示可大幅降低截断误差，为准粒子色散和多玻色连续谱提供定量可靠的描述。
英文摘要
Spin-wave theory provides a quasiparticle description of excitation spectra in quantum spin systems. In this theory, the spin operators are usually bosonized by the Holstein-Primakoff transformation or the Dyson-Maleev transformation. In practical calculations, the bosonized Hamiltonian has to be truncated, and thus the resulting excitation spectra depend on the choice of bosonic representation. Here, we introduce a generalized Holstein-Primakoff transformation that continuously interpolates between the conventional Holstein-Primakoff and Dyson-Maleev transformations through a single parameter. The formulation naturally extends to the SU(N) algebra and provides a flexible framework for optimizing bosonic truncations beyond harmonic order. As an application, we investigate the spin-1 bilinear-biquadratic model on the square lattice. By combining the generalized Holstein-Primakoff transformation with continuous similarity transformations, we obtain excitation spectra in excellent agreement with tensor-network calculations. Our results demonstrate that optimizing the bosonic representation substantially reduces truncation errors and provides quantitatively reliable descriptions of both quasiparticle dispersions and multi-boson continua.
