AI 中文总结
研究二维和三维自旋纹理在簇平均场近似中的量子特性，结合CMFA与对称化程序，利用磁构型圆柱对称性构建链状簇，揭示经典微磁模型局限，表明正则化微磁方程可作扩展框架。
AI 中文摘要
我们在簇平均场近似（CMFA）中研究二维和三维自旋纹理——$k\pi$ - 斯格明子和霍普夫离子环的量子特性。通过将CMFA与对称化程序相结合，取得两项关键进展：准确计算大自旋纹理中的量子涨落以及可靠获取亚稳态。利用所研究磁构型的圆柱对称性构建一维链状簇，用密度矩阵重整化群方法有效模拟，簇间相互作用在平均场水平处理。量子特征的空间分布揭示经典微磁模型的局限性及扩展必要性，表明正则化微磁方程为此提供合适框架。
英文摘要
We study the quantum properties of two- and three-dimensional spin textures -- $kπ$-skyrmions and hopfion rings -- within the cluster mean-field approximation (CMFA). By combining the CMFA with a symmetrization procedure, we achieve two key advances: the accurate computation of quantum fluctuations in large spin textures and reliable access to metastable states. These challenges are generally insurmountable using standard methods, which are severely limited by the curse of dimensionality and typically restricted to ground-state properties. Exploiting the cylindrical symmetry of the studied magnetic configurations, we construct one-dimensional chain-like clusters that can be efficiently simulated using the density matrix renormalization group method, while inter-cluster interactions are treated at the mean-field level. The resulting spatial profiles of quantum features such as the local variation of the magnetization length in hopfion rings reveal limitations of the classical micromagnetic model and indicate the necessity of its extension. We demonstrate that the recently proposed regularized micromagnetic equation provides a suitable framework for this purpose.
Comments10 pages, 4 figures
