发表机构
Indian Institute of Technology Kharagpur（印度理工学院卡拉格普尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于三阶 Bargmann 不变量的有限态框架，直接在离散参数空间评估陈数并刻画局部几何，应用于多种拓扑模型，无需动力学演化。
AI 中文摘要
我们开发了一个基于三阶 Bargmann 不变量的有限态几何框架，用于评估陈数并刻画局部量子态几何。利用规范不变的态重叠，该框架直接在离散参数空间上评估陈数，同时通过相位导出密度和互补振幅密度保留局部几何信息，以及与拓扑特征变化相关的签名。我们将该构造应用于 Qi-Wu-Zhang、$1/3$- 和 $1/4$-通量 Hofstadter、SSH 和 Rice-Mele 模型，包括用于孤立复合子空间的秩-$2$ 扩展，以及应用于闭环和参数空间拓扑。所得框架直接从有限态数据组织陈拓扑和局部几何信息，提供了一种紧凑的基于态的描述，而无需依赖动力学演化。
英文摘要
We develop a finite-state geometric framework based on third-order Bargmann invariants for evaluating Chern numbers and characterizing local quantum-state geometry. Using gauge-invariant state overlaps, the framework evaluates the Chern number directly on discretized parameter spaces while retaining local geometric information through the phase-derived density and the complementary amplitude density, as well as signatures associated with changes in topological character. We apply the construction to the Qi--Wu--Zhang, $1/3$- and $1/4$-flux Hofstadter, SSH, and Rice--Mele models, including a rank-$2$ extension for isolated composite subspaces and applications to closed-loop and parameter-space topology. The resulting framework organizes Chern topology and local geometric information directly from finite-state data, providing a compact state-based description without relying on dynamical evolution.
Comments22 pages, 13 figures
