Topological quantum numbers in the Hall effect

从拓扑指数看Laughlin态的分形霍尔电导

Fractional Hall Conductance of Laughlin States from a Topological Index

该研究通过严格的Laughlin泵论证，结合纯态对的指数与无限矩阵乘积态分析，确立了Laughlin态作为拓扑指数的分形霍尔电导量子化，证明其为拓扑稳定的分数量子霍尔相代表。

Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros

It has been shown that different Abelian and non-Abelian fraction quantum Hall states can be characterized by patterns of zeros described by sequences of integers {S_a}. In this paper, we will show how to use the data {S_a} to calculate various topological properties of the corresponding fraction quantum Hall state, such as the number of possible quasiparticle types and their quantum numbers, as well as the actions of the quasiparticle tunneling and modular transformations on the degenerate ground states on torus.

识别分数量子反常霍尔系统中的任意子拓扑序

Identifying Anyonic Topological Order in Fractional Quantum Anomalous Hall Systems

该研究通过代数拓扑方法确定分数量子反常霍尔系统中任意子的结构，揭示了其与陈数相关的编织相位特性，为理解拓扑序提供了理论基础。