作为能带几何与拓扑局部坐标的相对杂化纹理
Relative hybridization textures as local coordinates for band geometry and topology
AI总结：
研究提出用相对杂化坐标\(Z\)连接能带全局量与局部自由度，它能重构局部投影算符。在有效坐标片上其纹理编码多种物理量，坐标片障碍对应秩降缺陷。通过QWZ和晶格BHZ模型验证，为能带几何拓扑与微观结构联系提供扇区分辨框架。
AI中文摘要：
诸如贝里曲率和量子度量等全局诊断表征了占据的布洛赫子空间的几何与拓扑，却使承载此结构的微观扇区隐含。我们引入相对杂化坐标\(Z\)作为一种投影算符级诊断，将这些全局量与局部自由度相连。作为相对于选定扇区的格拉斯曼图坐标，\(Z\)重构局部投影算符并保留普通权重或胖带描述中缺失的相位和矩阵取向。在有效的坐标片上，其动量空间纹理编码贝里曲率、量子度量、贝里相位和威尔逊回路，坐标片障碍表现为秩降缺陷，\(\det Z\)的平衡坐标片缠绕给出第一陈数。在QWZ模型中，此缺陷清单重现陈相图。在晶格BHZ模型中，矩阵\(Z\)将轨道\(E|H\)划分诊断为量子自旋霍尔几何的稳健匹配坐标片，而自旋划分对块和\(\mathbb Z_2\)解释仍至关重要，并在自旋守恒极限下作为匹配坐标片显示秩亏缺。相对杂化坐标因此提供了一个扇区分辨框架，用于将能带几何与拓扑与微观结构联系起来。
英文摘要：
Global diagnostics such as Berry curvature and quantum metrics characterize the geometry and topology of an occupied Bloch subspace, leaving the microscopic sectors that carry this structure implicit. We introduce the relative hybridization coordinate $Z$ as a projector-level diagnostic connecting these global quantities to local degrees of freedom. As the Grassmann graph coordinate relative to a chosen sector, $Z$ reconstructs the local projector and retains the phase and matrix orientation absent from ordinary weight or fat-band descriptions. On valid chart patches, its momentum-space texture encodes Berry curvature, quantum metric, Berry phases, and Wilson loops, while chart obstructions appear as rank-drop defects whose balanced-chart winding of $\det Z$ gives the first Chern number. In the QWZ model this defect inventory reproduces the Chern phase diagram. In the lattice BHZ model, matrix $Z$ diagnoses the orbital $E|H$ partition as a robust matched chart for the QSH geometry, while the spin partition remains essential to the block and $\mathbb Z_2$ interpretation and shows rank deficiency as a matched chart in the spin-conserving limit. The relative hybridization coordinate thus provides a sector-resolved framework for relating band geometry and topology to microscopic structure.
