A unified framework for the Kondo problem and for an impurity in a Luttinger liquid
A unified framework for the Kondo problem and for an impurity in a Luttinger liquid
复制标题
近藤问题和 Luttinger 液体中杂质的统一框架
DOI：
10.1007/bf02175563
复制
发表时间：
1995
影响因子：
1.6
通讯作者：
H. Saleur
中科院分区：
文献类型：
--
作者：
P. Fendley;F. Lesage;H. Saleur
我们为各向异性Kondo模型和边界sine-Gordon模型建立了一个统一的理论框架。它们都是边界可积的量子场论，在边界上有一个量子群自旋，分别取量子群SU（2）q的标准或循环表示的值。这种统一是强大的，并允许我们找到两个模型的新结果。对于各向异性的近藤问题，我们发现精确的表达式（在磁场的存在下）的安德森-尤瓦尔微扰展开的所有系数。我们的表达式最初在非常各向异性的制度，但我们展示了如何继续他们超越图卢兹点所有的方式使用模拟的尺寸正则化的各向同性点。解析结构是透明的，只涉及简单的极点，我们确定的，连同他们的残留物。对于边界正弦戈登模型，它描述了一个杂质在Luttinger液体中，我们发现的非平衡电导的所有值的Luttinger耦合。这是一个复杂的计算，因为电压算子和边界散射不相互交换。
We develop a unified theoretical framework for the anisotropic Kondo model and the boundary sine-Gordon model. They are both boundary integrable quantum field theories with a quantum-group spin at the boundary which takes values, respectively, in standard or cyclic representations of the quantum groupSU(2)q. This unification is powerful, and allows us to find new results for both models. For the anisotropic Kondo problem, we find exact expressions (in the presence of a magnetic field) for all the coefficients in the Anderson-Yuval perturbative expansion. Our expressions hold initially in the very anisotropic regime, but we show how to continue them beyond the Toulouse point all the way to the isotropic point using an analog of dimensional regularization. The analytic structure is transparent, involving only simple poles which we determine exactly, together with their residues. For the boundary sine-Gordon model, which describes an impurity in a Luttinger liquid, we find the nonequilibrium conductance for all values of the Luttinger coupling. This is an intricate computation because the voltage operator and the boundary scattering do not commute with each other.