Dynamical spin-spin correlation functions in the Kondo model out of equilibrium
Dynamical spin-spin correlation functions in the Kondo model out of equilibrium
复制标题
近藤模型中的动态自旋相关函数失去平衡
DOI：
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
H. Schoeller
中科院分区：
文献类型：
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作者：
D. Schuricht;H. Schoeller
我们计算了与保持在不同化学势的两个非相互作用引线耦合的近藤点的动态自旋相关函数。为此，我们推广了最近开发的频率空间中的实时重整化群方法（RTRG-FS），以允许计算描述自旋和/或轨道波动的系统中任意点算子的动态相关函数。由此产生的双环 RG 方程在弱耦合状态下进行解析求解。这意味着只要通过点的电压 $V$ 或外部磁场 $h_0$ 足够大，$\max\{V,h_0\}\gg T_K$ 即可应用该方法，其中近藤温度 $T_K$ 是系统进入强耦合状态的尺度。明确地，我们计算了纵向和横向自旋-自旋相关性和响应函数以及由此产生的波动耗散比。实频率空间中的相关函数可以在松原空间中计算，而不需要任何解析延拓。我们获得了线形、小频率和大频率限制以及其他几个特征的分析结果，例如 $\Omega\approx\tilde{h}$ 处横向磁化率峰值的高度和宽度，其中 $\tilde{h}$ 表示减少的磁场。此外，我们讨论了如何推广所开发的方法来计算涉及储层自由度的其他算子的动态相关函数。
We calculate the dynamical spin-spin correlation functions of a Kondo dot coupled to two noninteracting leads held at different chemical potentials. To this end we generalize a recently developed real-time renormalization group method in frequency space (RTRG-FS) to allow the calculation of dynamical correlation functions of arbitrary dot operators in systems describing spin and/or orbital fluctuations. The resulting two-loop RG equations are analytically solved in the weak-coupling regime. This implies that the method can be applied provided either the voltage $V$ through the dot or the external magnetic field $h_0$ are sufficiently large, $\max\{V,h_0\}\gg T_K$, where the Kondo temperature $T_K$ is the scale where the system enters the strong-coupling regime. Explicitly, we calculate the longitudinal and transverse spin-spin correlation and response functions as well as the resulting fluctuation-dissipation ratios. The correlation functions in real-frequency space can be calculated in Matsubara space without the need of any analytical continuation. We obtain analytic results for the line-shape, the small- and large-frequency limits and several other features like the height and width of the peak in the transverse susceptibility at $\Omega\approx\tilde{h}$, where $\tilde{h}$ denotes the reduced magnetic field. Furthermore, we discuss how the developed method can be generalized to calculate dynamical correlation functions of other operators involving reservoir degrees of freedom as well.
影响因子：
8.6
作者：
C.-H. Chung;K. LeHur;M. Vojta;P. Wölfle
通讯作者：
P. Wölfle