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Topological approach to electron correlations at fractional quantum Hall effect
Annals of Physics ( IF 3 ) Pub Date : 2021-05-03 , DOI: 10.1016/j.aop.2021.168493
Janusz E. Jacak

The classification of homotopy invariants in interacting multi-electron 2D systems at quantizing magnetic fields is presented, explaining the topologically protected correlations occurring at integer and fractional quantum Hall effects. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to the binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants, which are universal and robust against local disorder and single-particle crystal field, as illustrated by experimental observations in various materials with different microscopic structure, like GaAs 2DES, graphene monolayer and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to single-particle perturbations, temperature chaos and variation of the electron interaction strength. The nonzero repulsive interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.



中文翻译:

分数量子霍尔效应下电子相关的拓扑方法

介绍了在相互作用的多电子2D系统中对磁场进行量化时的同构不变性的分类,从而解释了在整数和分数量子霍尔效应下发生的拓扑保护的相关性。与同位相相关的相位相比,长距离量子纠缠是必不可少的,而常规相位具有局部顺序参数的二进制纠缠则是不可或缺的。由电子的库仑相互作用诱导的同构远程相关相的分类是根据同构不变量推导的,这些同构不变量对于局部无序和单粒子晶体场具有普遍性和鲁棒性,如各种材料的实验观察所表明的那样。微观结构,例如GaAs 2DES,石墨烯单层和双层以及在Chern拓扑绝缘体中。证明同型相在拓扑上受到保护,并且不受单粒子扰动,温度混乱和电子相互作用强度变化的影响。然而,电子之间的非零排斥相互作用被证明对于定义同构不变量是必不可少的,同构不变量在气体系统中消失。

更新日期:2021-05-08
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