标题： 扭曲MoTe$_2$晶格模型中的分数量子霍尔绝缘体及竞争态 显示英文标题

标题： Fractional Chern Insulators and Competing States in a Twisted MoTe$_2$ Lattice Model

摘要： 我们构建了一个相互作用的晶格模型，用于研究扭曲角度约为 3.7\degree 的$\mathrm{MoTe}_{2}$双层结构。 我们使用圆柱几何中的无限密度矩阵重整化群（iDMRG）来识别多种竞争性的整数和分数陈绝缘体以及由谷极化自发打破时间反演对称性后出现的电荷密度波（CDW）态。 我们通过有限尺寸分析证实了即使在允许竞争性 CDW 几何结构中，陈绝缘态的鲁棒性，并探索了这些态之间由增加的亚晶格势能或相互作用强度驱动的相变。 我们的工作强调了直接自旋交换在稳定母谷极化陈铁磁带中的关键作用，以及与高能带混合在促进 CDW 序替代 CIs/FCIs 中的破坏作用。 显示英文摘要

摘要： We construct an interacting lattice model for twisted $\mathrm{MoTe}_{2}$ bilayers at a twist angle of approximately 3.7\degree. We use the infinite density matrix renormalization group (iDMRG) in a cylinder geometry to identify a variety of competing integer and fractional Chern insulators and charge density wave (CDW) states that emerge upon the spontaneous breaking of time reversal symmetry by valley polarization. We use finite-size analysis to establish the robustness of Chern insulating states even in geometries that admit competing CDWs, and explore the phase transitions between these states driven by increasing sublattice potential or interaction strength. Our work highlights the crucial role played by direct spin exchange in stabilizing the parent valley-polarized Chern ferromagnet band, and by the mixing with higher bands in destabilizing CIs/FCIs in favor of CDW orders.