论文标题
手性数值重归其化群
Chiral numerical renormalization group
论文作者
论文摘要
已经广泛研究了量子杂质(通过它们夫妇介导的电子通道)的近杂质筛选(通过它们夫妇的电子通道)之间的相互作用(由同一通道介导的)。然而,单向通道(例如,2D拓扑材料的手性或螺旋边缘模式)极大地限制了介导的际交往相互作用的影响,最近才受到审查,并且可以极大地改变物理。在这里,我们采用Wilson的数值重归其化组(NRG),这是治疗量子杂质模型的最成熟的数值方法,并将其扩展到由在不同位置耦合到单向通道的两个杂质组成的系统。由于单向与NRG中的主要成分之一(将通道映射到Wilson链的映射),这是一条具有杂质的紧密结合链,并跳出振幅,这是一个紧密的结合链,这是一个具有挑战性的。我们通过引入一个由两个耦合的威尔逊连锁店组成的“威尔逊梯子”来弥合这一差距,并证明该结构成功捕获了通道的单向性,以及两种杂质之间的距离。我们使用此映射来研究两个近杂质杂质与单个手性通道耦合,表明所有局部性能和热力学量对际冲突距离无关,并且对应于两个单独的单个单个模型。可能会扩展到更多的杂质和/或螺旋通道。
The interplay between the Kondo screening of quantum impurities (by the electronic channels to which they couple) and the interimpurity RKKY interactions (mediated by the same channels) has been extensively studied. However, the effect of unidirectional channels (e.g., chiral or helical edge modes of 2D topological materials) which greatly restrict the mediated interimpurity interactions, has only more recently come under scrutiny, and it can drastically alter the physics. Here we take Wilson's numerical renormalization group (NRG), the most established numerical method for treating quantum impurity models, and extend it to systems consisting of two impurities coupled at different locations to unidirectional channel(s). This is challenging due to the incompatibility of unidirectionality with one of the main ingredients in NRG -- the mapping of the channel(s) to a Wilson chain -- a tight-binding chain with the impurity at one end and hopping amplitudes which decay exponentially with the distance. We bridge this gap by introducing a "Wilson ladder" consisting of two coupled Wilson chains, and demonstrate that this construction successfully captures the unidirectionality of the channel(s), as well as the distance between the two impurities. We use this mapping in order to study two Kondo impurities coupled to a single chiral channel, showing that all local properties and thermodynamic quantities are indifferent to the interimpurity distance, and correspond to two separate single-impurity models. Extensions to more impurities and/or helical channels are possible.