分数陈绝缘体的拓扑激发与量子相变

Recently, the study of fractional Chern insulators, also called fractional quantum anomalous Hall states, has become an important research frontier area of international condensed matter physics community. Exact numerical calculations and theoretical studies demonstrated that fractional Chern insulators can be realized in two-dimensional strongly correlated lattice systems with topological flat bands. Fractional Chern insulators exhibit similar fractionalization phenomena as the conventional fractional quantum Hall systems. This project aims to study topological excitations and quantum phase transitions of fractional Chern insulators. The main research contents and research goals are: exotic topological excitations in fractional Chern insulators with high Chern numbers; charge fractionalization and topological excitations of fractional Chern insulators in singular geometries; topological quantum phase transitions between fractional Chern insulators and other topological quantum states; topological quantum phase transitions of fractional Chern insulators in singular geometries. We adopt the numerical methods based upon exact diagonalizations, and the numerical constructions of topological quantum many-body wave functions. We aim to open one or two new research directions in this field.

近年来，分数陈绝缘体，也称分数量子反常霍尔态，已经成为国际凝聚态物理学界的重要前沿研究领域。严格的数值计算和理论研究表明：含有拓扑平带的二维晶格中的强关联体系可以实现分数陈绝缘体，分数陈绝缘体与传统的分数量子霍尔态有类似的分数化现象。本项目拟研究分数陈绝缘体的拓扑激发与量子相变，研究内容与研究目标等如下：高陈数分数陈绝缘体的异常拓扑激发；奇异几何结构上分数陈绝缘体的分数化电荷与拓扑激发；分数陈绝缘体与其他拓扑量子态的拓扑量子相变；奇异几何结构上分数陈绝缘体的拓扑量子相变。研究手段基于严格对角化的精确数值方法，拓扑量子多体波函数数值构造方法等。我们争取再次开辟一到两个新的前沿子领域。

在该研究项目执行中，我们取得如下代表性研究成果：发现奇异几何的分数陈绝缘体；准晶型体系中的陈绝缘体；碟形结构中的非阿贝尔分数陈绝缘体；填充数1/2的玻色分数陈绝缘体的量子相变；陈绝缘体莫比乌斯带的量子输运；整数填充多带系统的玻色分数陈绝缘体；呼吸笼目晶格模型的拓扑量子相变；具有交错磁通的二聚化体系中的异常拓扑态。该项目研究成果一方面发展了分数拓扑态多体波函数的数值方法，加深了对分数陈绝缘体态的拓扑序与量子相变特性的了解；另一方面给出多种陈绝缘体、二阶拓扑态、异常拓扑态之间拓扑量子相变的丰富相图以及特殊的拓扑输运特性。