标题： 扭曲MoTe$_2$中的分数陈绝缘体和量子异常霍尔晶体 显示英文标题

标题： Fractional Chern Insulator and Quantum Anomalous Hall Crystal in Twisted MoTe$_2$

摘要： 近期的实验进展在扭曲的二硒化钼（tMoTe$_2$）体系中发现了分数陈绝缘体，这在理解相互作用效应和相关的拓扑相方面带来了重大的理论挑战。 在这里，我们构建了一个专门针对tMoTe$_2$的真实摩尔晶格模型，并使用最先进的张量网络方法进行研究。 我们的基态计算揭示了丰富的与相互作用和填充相关的相，包括分数陈绝缘体（FCI）、陈绝缘体以及广义的温格尔晶体等，这些解释了最近的实验观测结果。 此外，我们揭示了在分数摩尔超胞填充下表现出整数量子霍尔电导的量子异常霍尔晶体，这为tMoTe$_2$中的实验探索开辟了新的途径。 在FCI相中，动力学模拟显示存在一个具有有限电荷间隙的单粒子连续谱，表明存在分数电荷激发。 此外，我们的有限温度计算确定了电荷激活和铁磁（FM）转变的特征温度，与实验结果一致。 我们发现电荷间隙远大于热激活和FM转变的能量尺度，这解释了最近的实验观察结果。 总体而言，通过整合tMoTe$_2$和相关系统中的基态、有限温度和动力学张量网络计算，我们建立了一个理论框架，用于理解和探索tMoTe$_2$及相关系统的关联拓扑相。 显示英文摘要

摘要： Recent experimental advances have uncovered fractional Chern insulators in twisted MoTe$_2$ (tMoTe$_2$) systems, posing significant theoretical challenges in understanding the interaction effects and correlated topological phases. Here, we construct a realistic moir\'e lattice model tailored for tMoTe$_2$ and conduct investigations using state-of-the-art tensor-network methods. Our ground-state calculations reveal a rich array of interaction- and filling-dependent phases, including the FCI, Chern insulator, and generalized Wigner crystal, etc., explaining recent experimental observations. Moreover, we reveal quantum anomalous Hall crystals exhibiting integer Hall conductivity at fractional moir\'e unit cell fillings, which opens new avenues for experimental exploration in tMoTe$_2$. In the FCI phase, dynamical simulations reveal a single-particle continuum with a finite charge gap, indicating the presence of fractional charge excitations. Moreover, our finite-temperature calculations determine the characteristic temperatures for charge activation and ferromagnetic (FM) transitions, consistent with experiments. We find that the charge gap is significantly larger than the energy scales of both thermal activation and FM transitions, explaining recent experimental observations. Overall, by integrating ground-state, finite-temperature, and dynamical tensor-network calculations on the real-space model, we establish a theoretical framework for understanding and exploring correlated topological phases in tMoTe$_2$ and related systems.