Real-time renormalization group in frequency space: A two-loop analysis of the nonequilibrium anisotropic Kondo model at finite magnetic field
Real-time renormalization group in frequency space: A two-loop analysis of the nonequilibrium anisotropic Kondo model at finite magnetic field
复制标题
频率空间中的实时重正化群：有限磁场下非平衡各向异性 Kondo 模型的双环分析
DOI：
10.1103/physrevb.80.045117
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发表时间：
2009
影响因子：
3.7
通讯作者：
F. Reininghaus
中科院分区：
文献类型：
--
作者：
H. Schoeller;F. Reininghaus
我们在频率空间中应用最近开发的非平衡实时重整化群（RG）方法来描述通过自旋和/或轨道涨落与多个储库弱耦合的小型费米子量子系统的非线性量子输运。在弱耦合二环分析中，我们推导了非线性电导的解析公式和确定约简密度矩阵的时间演化的核。提出了一致的形式主义如何通过弛豫和相移速率来切断 RG 流。我们将一般形式应用于有限磁场下的非平衡各向异性 Kondo 模型。我们考虑弱耦合状态，其中电压和裸磁场的最大值大于近藤温度。在这种情况下，我们计算非线性电导、磁化率、重整化自旋弛豫和移相速率以及重整化 $g$ 因子。所有量均被考虑到超出共振主阶的第一个对数校正。在重新定义近藤温度之前，我们确认了先前在各向同性情况下的电导率和磁化率的结果。此外，我们提出了共振线形状的一致计算，包括确定自旋弛豫或移相率是否切断对数发散。此外，我们还计算了表征磁化强度随时间演化的指数衰减的量。与电导相反，我们发现，对于比重整化磁场更小（更大）的电压，自旋弛豫（移相）速率相对于磁场的导数呈对数增强（抑制），并且对数发散被相反的速率截断。重整化的 $g$ 因子预计会在共振时显示对称对数抑制，该抑制被自旋弛豫率切断。我们提出了一种三端装置来测量谐振抑制。对于所有量，我们还分析了各向异性情况，并发现了共振时的其他非平衡效应。
We apply a recently developed nonequilibrium real-time renormalization group (RG) method in frequency space to describe nonlinear quantum transport through a small fermionic quantum system coupled weakly to several reservoirs via spin and/or orbital fluctuations. Within a weak-coupling two-loop analysis, we derive analytic formulas for the nonlinear conductance and the kernel determining the time evolution of the reduced density matrix. A consistent formalism is presented how the RG flow is cut off by relaxation and dephasing rates. We apply the general formalism to the nonequilibrium anisotropic Kondo model at finite magnetic field. We consider the weak-coupling regime, where the maximum of voltage and bare magnetic field is larger than the Kondo temperature. In this regime, we calculate the nonlinear conductance, the magnetic susceptibility, the renormalized spin relaxation and dephasing rates, and the renormalized $g$ factor. All quantities are considered up to the first logarithmic correction beyond leading order at resonance. Up to a redefinition of the Kondo temperature, we confirm previous results for the conductance and the magnetic susceptibility in the isotropic case. In addition, we present a consistent calculation of the resonant line shapes, including the determination whether the spin relaxation or dephasing rate cuts off the logarithmic divergence. Furthermore, we calculate quantities characterizing the exponential decay of the time evolution of the magnetization. In contrast to the conductance, we find that the derivative of the spin relaxation (dephasing) rate with respect to the magnetic field is logarithmically enhanced (suppressed) for voltages smaller (larger) than the renormalized magnetic field, and that the logarithmic divergence is cut off by the opposite rate. The renormalized $g$ factor is predicted to show a symmetric logarithmic suppression at resonance, which is cut off by the spin relaxation rate. We propose a three-terminal setup to measure the suppression at resonance. For all quantities, we analyze also the anisotropic case and find additional nonequilibrium effects at resonance.