AI 中文总结
本研究提出中心装饰 kagome 模型，通过调控中心位点跃迁 t₂ 优化量子几何，成功稳定了 ν=1/3 和 ν=1/5 填充的稀释分形陈绝缘体，为相关研究提供了新的调控思路。
AI 中文摘要
分形陈绝缘体作为无朗道能级的分数量子霍尔态的晶格类似物，已引起广泛关注。然而，低填充率的分形陈绝缘体较为脆弱，因为电荷有序相与分形拓扑液体存在强烈竞争。本文基于几何可调人工晶格，提出中心装饰 kagome 模型，其中中心位点跃迁 t₂ 为孤立 C=1 平带的量子几何提供了直接调控旋钮，量子几何指决定陈带内相互作用形状因子的贝里曲率和富比尼-施图迪度量。精确对角化结果显示，将 t₂ 从平带优化的 kagome 极限调开，可减少迹条件偏差、抑制竞争电荷有序相，并在 ν=1/3 和更脆弱的 ν=1/5 填充时提升多体稳定性。在 ν=1/5 时，该稳定性增强窗口在邻近相互作用分布下仍存在，包括主导第三近邻排斥的变化和弱近邻混合。低能谱、谱流、准空穴与纠缠计数、静态结构因子以及量化总多体陈数 C_tot=1 均一致支持类劳克林分形陈绝缘体。这些结果表明，量子几何工程是仅靠带平坦度优化之外，稳定稀释分形陈绝缘体的一条途径。
英文摘要
Fractional Chern insulators have attracted broad interest as lattice analogs of fractional quantum Hall states without Landau levels. However, low-filling fractional Chern insulators are fragile because charge-ordered phases can compete strongly with the fractional topological liquid. Here, we propose a center-decorated kagome model, motivated by geometry-tunable artificial lattices, in which the center-site hopping $t_2$ provides a direct knob for the quantum geometry of an isolated $C=1$ flat band. Here quantum geometry refers to the Berry curvature and Fubini--Study metric, which determine the form factors of interactions projected into the Chern band. Exact diagonalization shows that tuning $t_2$ away from the flatness-optimized kagome limit reduces the trace-condition deviation, suppresses competing charge order, and enhances the many-body stability at both $ν=1/3$ and the more fragile $ν=1/5$ filling. At $ν=1/5$, this stability-enhanced window persists under nearby interaction profiles, including variations of the dominant third-neighbor repulsion and weak nearest-neighbor admixtures. Low-energy spectra, spectral flow, quasihole and entanglement counting, static structure factors, and the quantized total many-body Chern number $C_{\mathrm{tot}}=1$ consistently support Laughlin-like fractional Chern insulators. These results identify quantum-geometry engineering as a route to stabilizing dilute fractional Chern insulators beyond band-flatness optimization alone.
