论文标题
模型分数Chern绝缘子在所有拓扑理想的平带中的起源
Origin of Model Fractional Chern Insulators in All Topological Ideal Flatbands: Explicit Color-entangled Wavefunction and Exact Density Algebra
论文作者
论文摘要
人们普遍认为，非均匀的浆果曲率会破坏吉尔文·麦克唐纳 - 普拉茨曼代数，因此破坏了分数Chern绝缘子的稳定性。在这项工作中，我们通过为所有具有非零的Chern数量的拓扑理想的平板提出理论来反驳这一共同的知识。光滑的单粒子Bloch波函数被证明可以接收一种确切的颜色键入形式，作为C最低界限级别的层次的叠加。包括排斥性相互作用，Halperin类型的Abelian和非阿布尔模型分数切绝缘子被稳定，因为无论质量几何形状是理想的，并且排斥力是短量的，因此无论剩余的浆果曲率多么不均匀，无论是零均匀的浆果曲率，无论是零均匀的基础状态。背后的关键原因是存在一个新兴的希尔伯特空间，在该空间中，可以通过调整波函数的归一化来使浆果曲率完全扁平。在这样的空间中，平面项目的密度操作员服从封闭的吉尔文 - 麦克唐纳 - 普拉茨曼型代数，使精确的映射到C层的Landau级别。最后，我们讨论了该理论对Moire悬带系统的应用，该系统特别关注分数化相位和自发对称性破坏阶段，该阶段最近在基于石墨烯的扭曲材料中观察到。
It is commonly believed that nonuniform Berry curvature destroys the Girvin-MacDonald-Platzman algebra and as a consequence destabilizes fractional Chern insulators. In this work we disprove this common lore by presenting a theory for all topological ideal flatbands with nonzero Chern number C. The smooth single-particle Bloch wavefunction is proved to admit an exact color-entangled form as a superposition of C lowest Landau level type wavefunctions distinguished by boundary conditions. Including repulsive interactions, Abelian and non-Abelian model fractional Chern insulators of Halperin type are stabilized as exact zero-energy ground states no matter how nonuniform Berry curvature is, as long as the quantum geometry is ideal and the repulsion is short-ranged. The key reason behind is the existence of an emergent Hilbert space in which Berry curvature can be exactly flattened by adjusting wavefunction's normalization. In such space, the flatband-projected density operator obeys a closed Girvin-MacDonald-Platzman type algebra, making exact mapping to C-layered Landau levels possible. In the end we discuss applications of the theory to moire flatband systems with a particular focus on the fractionalized phase and spontaneous symmetry breaking phase recently observed in graphene based twisted materials.
