广义BHZ模型中的鲁棒拓扑与可调几何：具有分数阶色散

中文摘要 AI 辅助

随着分数阶量子力学的最新发展，我们引入了伯尼格-休斯-张（BHZ）模型的分数阶推广，以研究分数阶色散对能带拓扑和量子几何的影响。在低能极限下，该模型简化为分数阶狄拉克哈密顿量，同时保持动量空间周期性，从而确保紧凑的布里渊区和定义良好的拓扑不变量。我们进一步表明，相应的实空间紧束缚模型可以通过傅里叶级数变换直接构造，为通常用于分数阶晶格系统的方法提供了一种更简单且更通用的替代方案。这种方法很容易扩展到本文所考虑的广义BHZ模型之外。利用布洛赫本征态，我们计算了量子几何张量并分析了其分量，即贝里曲率和量子度量。我们发现，当色散指数变为分数时，分数阶调谐会重新分布这些量在整个布里渊区中的值，导致局部能带几何发生显著变化。相比之下，陈数保持不变，证明了全局拓扑相在分数阶变形下的鲁棒性。我们进一步论证，这种不变性对于一大类分数阶模型持续存在。

英文摘要

With recent developments in fractional quantum mechanics, we introduce a fractional generalization of the Bernevig-Hughes-Zhang (BHZ) model to investigate the effects of fractional dispersion on band topology and quantum geometry. In the low-energy limit, the model reduces to a fractional Dirac Hamiltonian while preserving momentum-space periodicity, thereby ensuring a compact Brillouin zone and a well-defined topological invariant. We further show that the corresponding real-space tight-binding model can be constructed directly through a Fourier-series transformation, providing a simpler and more general alternative to the methods typically employed for fractional lattice systems. This approach readily extends beyond the generalized BHZ model considered here. Using the Bloch eigenstates, we compute the quantum geometric tensor and analyze its components, namely the Berry curvature and quantum metric. We find that fractional tuning redistributes these quantities throughout the Brillouin zone as the dispersion exponent becomes fractional, leading to pronounced modifications of the local band geometry. In contrast, the Chern number remains invariant, demonstrating the robustness of the global topological phase against fractional deformation. We further argue that this invariance persists for a broad class of fractional models.

发表机构

• National Institute of Physics, University of the Philippines Diliman（菲律宾大学迪利曼分校国家物理研究所）

机构由 AI 辅助整理，请以论文原文为准。

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9 pages, 3 figures