AI 中文总结
研究人员在负曲率双曲晶格上构建异常弗洛凯拓扑相，通过穿孔周期双曲晶格的谱流诊断方法，识别出手性边界模式，为拓扑双曲系统研究提供了新手段。
AI 中文摘要
我们在负曲率双曲晶格上构建了一种异常弗洛凯拓扑相。该模型是一个紧束缚哈密顿量，具有周期性重复的四色边跳跃序列和子晶格交错的 onsite 势阶。当单个跳跃步完全将振幅转移过一个活性边时，达到拓扑 regime；当单个跳跃步期间沿活性边发生两次完整跳跃，使振幅返回起始位点时，达到平庸 regime。在有限开放 patch 中，拓扑 regime 的特征是在 0 和 π 处存在体准能隙，且隙内填充了隙内态，而平庸 regime 中这些隙为空。我们利用紧凑周期晶格绘制了体 0 和 π 准能隙图，确定了与平庸和异常开放边界谱相连的带隙区域，并通过实空间动力学将隙内态判定为手性边界模式。最后，我们引入了一种基于穿孔周期双曲晶格的小边界谱流诊断方法，该方法可避免有限双曲 patch 广泛外边界带来的歧义，有望用于研究其他拓扑双曲系统。
英文摘要
We construct an anomalous Floquet topological phase on a negatively curved hyperbolic lattice. The model is a tight-binding Hamiltonian with a periodically repeated four-color edge-hopping sequence and a sublattice-staggered onsite potential step. The topological regime is reached near the limit in which a single hopping step transfers amplitude completely across an active edge, while the trivial regime is reached near the point where two full hops occur along an active edge during a single hopping step, returning the amplitude to its starting site. In finite open patches, the topological regime is characterized by bulk quasienergy gaps at $0$ and $π$ that are populated by in-gap states, in contrast to a trivial regime where these gaps remain empty. Using compact periodic lattices, we map the bulk $0$ and $π$ quasienergy gaps and identify the gapped regions connected to the trivial and anomalous open-boundary spectra. We diagnose the in-gap states as chiral boundary modes by their real-space dynamics. Finally, we introduce a small-boundary spectral-flow diagnostic based on punctured periodic hyperbolic lattices, which avoids the ambiguity associated with the extensive outer boundary of finite hyperbolic patches. This puncture-based diagnostic should be useful for studying other topological hyperbolic systems.
Comments15 pages, 11 figures
