Dynamical spin-spin correlation functions in the Kondo model out of equilibrium

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 (RG) method in frequency space [H. Schoeller, Eur. Phys. J. Spec. Top. 168, 179 (2009)] 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 h₀ are sufficiently large, maxV,h₀TK, where the Kondo temperature TK 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 Ω≈ ̃ \~h, where ̃ \~h denotes the renormalized 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.