AI 中文总结
本研究提出最优嵌入紧束缚框架，将轨道嵌入项作为可调参数，构建的GaAs、CdS模型可定量重现非线性光学响应且不损失能带结构精度，还揭示了几何对局部度量迹的显著影响。
AI 中文摘要
在紧束缚模型中，位置算子被简化为晶胞内轨道位置（嵌入项）。这类模型虽能准确重现能带结构，但在依赖位置算子的几何相关响应上常失效。为解决此问题，我们研究了这些嵌入项的作用并提出最优嵌入紧束缚的通用框架。将嵌入项视为几何调谐参数，通过与参考响应（从头算计算或实验获得）拟合确定，我们得到了GaAs和CdS的紧束缚模型，其能带结构精度未受损失，还能定量重现非线性光学响应。我们通过将紧束缚可观测量分解为几何无关和相关部分得到的位置导数高效确定最优嵌入项，并为量子几何张量等关键量提供了显式导数。该分解揭示了几何效应占主导的区域，我们在玩具模型和陈绝缘体V₂O₃中展示了几何如何显著改变局部度量迹。我们的结果强调，轨道嵌入项应被视为真正的模型参数，需针对物理数据显式确定，以获得准确的最小模型。
英文摘要
In tight-binding models, the position operator is reduced to intra-cell orbital positions (embeddings). While accurately reproducing band structures, such models often fail for geometry dependent responses depending on the position operator. To address this, we investigate the role of these embeddings and introduce the general framework of optimally embedded tight binding. Treating the embeddings as geometric tuning parameters to be fixed against a reference response (obtained from ab-initio computation or experiment), we obtain tight-binding models of GaAs and CdS which quantitatively reproduce non-linear optical responses at no cost to band structure accuracy. The optimal embeddings are determined efficiently using position derivatives obtained from decomposing tight-binding observables into a geometry independent and dependent part, and explicit derivatives are provided for key quantities such as the quantum geometric tensor. The decomposition reveals where geometric effects dominate, and we show in both toy models and in the Chern insulator V2O3 how geometry can dramatically alter the local metric trace. Our results highlight that orbital embeddings should be treated as a genuine model parameter which should be explicitly fixed against physical data to get accurate minimal models.
CommentsMain: 18 pages, 7 figures, Appendix: 10 pages, 6 figures
