发表机构
i Intelligent Insights; School of Physics and Optoelectronic Engineering, Nanjing University of Information Science and Technology（4i 智能洞察; 南京信息工程大学物理与光电工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究结合局域自旋期望值几何与谱微扰理论，为量子自旋织构在磁场扰动下的斯格明子电荷稳定性提供认证界，并通过七自旋例子验证了电荷改变与能隙保持的共存。
AI 中文摘要
磁场改变多少才会使量子自旋织构失去其斯格明子电荷？我们通过将局域自旋期望值的几何与谱微扰理论相结合来解决这个问题。对于三角剖分的自旋-$s$织构，我们确定了使其重构拓扑电荷变得不明确的局域矩的最小变化，允许不相等的误差界和固定的边界矩。这个几何阈值给出了保持基态电荷的磁场扰动的显式界，当能隙和几何余量具有正极限时，具有$1/N$标度。我们将这些界应用于具有交换和Dzyaloshinskii--Moriya相互作用的有限自旋-$1/2$系统。在一个经过严格验证的七自旋例子中，电荷在单个认证场处改变，而激发能隙和所有局域自旋极化保持远离零；在这样的交叉处，几何余量和场证书线性消失。这些结果提供了织构稳定性的定量证书，并阐明了谱能隙保护的局限性。
英文摘要
How much can a magnetic field change before a quantum spin texture loses its skyrmion charge? For a triangulated spin-$s$ texture on $N$ quantum sites, we determine the smallest change in its local moments that makes the reconstructed topological charge ill-defined, allowing unequal error bounds and fixed boundary moments. Combined with spectral perturbation theory, this geometric threshold yields explicit magnetic-field intervals that preserve the ground-state charge, scaling as $1/N$ when the gap and geometric margin have positive limits. We apply the bounds to finite spin-$1/2$ systems with exchange and Dzyaloshinskii-Moriya interactions. In a rigorously verified seven-spin example the charge changes at a single certified field, while the excitation gap and all local spin polarizations remain bounded away from zero; there the geometric margin vanishes linearly.
Comments20 pages, 3 figures. Title changed; references expanded; the sharpened rotation bound is now attributed to the Davis-Kahan sin 2Theta theorem; comparison with the quantum scalar chirality and with earlier work added; minor rewording
