近藤效应的全息模型
A Holographic Model of the Kondo Effect
摘要：
我们提出了一个基于反德西特/共形场论（AdS/CFT）对应的近藤效应模型，也被称为全息。近藤效应是一种磁性杂质在低温下与传导电子池反铁磁耦合的屏蔽效应。在（1+1）维CFT描述中，近藤效应是由具有相同Kac-Moody流代数的两个不动点之间的边缘相关（0+1）维算子触发的重整化群流.在大N极限下，在自旋SU（N）和电荷U（1）对称性下，近藤效应表现为（0+1）维的二阶平均场跃迁，其中U（1）电荷对称性自发破缺。我们的全息模型是（2+1）维AdS空间AdS 3中的Chern-Simons规范场，它与Kac-Moody电流对偶，并沿AdS 2子空间耦合到全息超导体。我们的模型表现出几个特征的近藤效应，包括动态生成的规模，在低温下的温度与幂律行为的电阻率，和光谱流产生相移。我们的全息近藤模型可能是有用的研究许多开放的问题，包括杂质，例如近藤晶格问题。
英文摘要：
We propose a model of the Kondo effect based on the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, also known as holography. The Kondo effect is the screening of a magnetic impurity coupled anti-ferromagnetically to a bath of conduction electrons at low temperatures. In a (1+1)-dimensional CFT description, the Kondo effect is a renormalization group flow triggered by a marginally relevant (0+1)-dimensional operator between two fixed points with the same Kac-Moody current algebra. In the large-N limit, with spin SU(N) and charge U(1) symmetries, the Kondo effect appears as a (0+1)-dimensional second-order mean-field transition in which the U(1) charge symmetry is spontaneously broken. Our holographic model, which combines the CFT and large-N descriptions, is a Chern-Simons gauge field in (2+1)-dimensional AdS space, AdS3, dual to the Kac-Moody current, coupled to a holographic superconductor along an AdS2 subspace. Our model exhibits several characteristic features of the Kondo effect, including a dynamically generated scale, a resistivity with power-law behavior in temperature at low temperatures, and a spectral flow producing a phase shift. Our holographic Kondo model may be useful for studying many open problems involving impurities, including for example the Kondo lattice problem.
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