标题： 分数量化电极化和晶体分数陈绝缘体的离散位移 显示英文标题

标题： Fractionally Quantized Electric Polarization and Discrete Shift of Crystalline Fractional Chern Insulators

摘要： 具有晶体对称性的分数陈绝缘体（FCI）具有拓扑不变量，这些不变量在连续分数量子霍尔（FQH）态中没有对应的类似物。 在这里，我们通过模型波函数的数值计算证明，FCIs 具有分数量子化的电极化率，$\vec{\mathscr{P}}_{\text{o}}$，其中$\text{o}$是一个高对称点。 与整数陈绝缘体允许的值相比，$\vec{\mathscr{P}}_{\text{o}}$由于任何子在晶格平移对称下可能携带分数量子数而取分数值。 $\vec{\mathscr{P}}_{\text{o}}$与离散位移$\mathscr{S}_{\text{o}}$一起，决定了包含晶格位错、位错、边界和/或角的区域中电荷的分数量子化普遍贡献，这些贡献是基本任何子电荷的分数。 我们展示了如何使用 Monte Carlo 计算，通过对带有晶格缺陷的模型波函数进行计算，提取 1/2-Laughlin 和 1/3-Laughlin FCIs 的不变量，分别在正方形和蜂窝晶格上通过部分子构造获得。 这些结果构成了一类超越三十年前发现的已知分数量子化响应特性的一类拓扑有序态的性质。 显示英文摘要

摘要： Fractional Chern insulators (FCI) with crystalline symmetry possess topological invariants that fundamentally have no analog in continuum fractional quantum Hall (FQH) states. Here we demonstrate through numerical calculations on model wave functions that FCIs possess a fractionally quantized electric polarization, $\vec{\mathscr{P}}_{\text{o}}$, where $\text{o}$ is a high symmetry point. $\vec{\mathscr{P}}_{\text{o}}$ takes fractional values as compared to the allowed values for integer Chern insulators because of the possibility that anyons carry fractional quantum numbers under lattice translation symmetries. $\vec{\mathscr{P}}_{\text{o}}$, together with the discrete shift $\mathscr{S}_{\text{o}}$, determine fractionally quantized universal contributions to electric charge in regions containing lattice disclinations, dislocations, boundaries, and/or corners, and which are fractions of the minimal anyon charge. We demonstrate how these invariants can be extracted using Monte Carlo computations on model wave functions with lattice defects for 1/2-Laughlin and 1/3-Laughlin FCIs on the square and honeycomb lattice, respectively, obtained using the parton construction. These results comprise a class of fractionally quantized response properties of topologically ordered states that go beyond the known ones discovered over thirty years ago.