AI 中文总结
研究对称二阶张量表示中的奇异现象，以电场梯度张量为原型，通过第一性原理计算利用应变控制其在张量空间变化，在多种材料中研究，区分局部报告奇点与全局本征框架拓扑，为局部重建返回奇偶性提供途径。
AI 中文摘要
对称二阶张量通过按大小排序的主值和轴来表示。这种表示折叠了张量空间，当一个主值穿过零或两个主值简并时，报告的参数会出现尖点并交换标签，隐藏了全局效应，如主轴上箭头绕简并点闭环传输会反向。我们以电场梯度（EFG）张量为原型，利用第一性原理计算确定施加应变可控制其在张量空间中的变化。在金红石TiO₂、SnO₂和立方MgO中进行研究，结果区分了局部报告奇点与全局本征框架拓扑，潜在光谱几何也适用于空间张量场，应变调谐、取向分辨超精细光谱可局部重建返回奇偶性。
英文摘要
Many observables are symmetric second-rank tensors, reported through magnitude-ordered principal values and axes. This chart folds tensor space: the parameters develop cusps and exchange labels where the tensor is smooth. It also hides a global effect: an arrow carried along a principal axis around a loop encircling a degeneracy can return reversed, defining a binary return parity, invariant under smooth deformations of the loop avoiding degeneracy. For tensor fields, this structure is long established, but the parameters are coordinates of the domain on which the field is defined, and the degeneracies are a feature of that particular field. Here we show that the electric field gradient (EFG) carries the same structure in a control space: a traceless observable at a single probe site, steered through its five-dimensional tensor space by symmetry-adapted strain, with the encircling loop applied rather than found. First-principles calculations reveal an isolated degeneracy with nontrivial parity in rutile TiO$_2$, point- or line-like degeneracies in SnO$_2$ depending on the control slice, and access to all five EFG components in cubic MgO. Thus, return parity becomes accessible for a local observable, and strain-tuned, orientation-resolved hyperfine spectroscopy offers a route to reconstruct it.
