Spatial and temporal propagation of Kondo correlations

We address the fundamental question how the spatial Kondo correlations are building up in time assuming an initially decoupled impurity spin (S) over right arrow (imp). We investigate the time-dependent spin-correlation function chi((r) over right arrow, t) = <(S) over right arrow (imp)(s) over right arrow((r) over right arrow)> in the Kondo model with antiferromagnetic and ferromagnetic couplings, where (s) over right arrow((r) over right arrow) denotes the spin density of the conduction electrons after switching on the Kondo coupling at time t = 0. We present data obtained from a time-dependent numerical renormalisation group (TD-NRG) calculation. We gauge the accuracy of our two-band NRG by the spatial sum rules of the equilibrium correlation functions and the reproduction of the analytically exactly known spin-correlation function of the decoupled Fermi sea. We find a remarkable building up of Kondo correlation outside of the light cone defined by the Fermi velocity of the host metal. By employing a perturbative approach exact in second-order of the Kondo coupling, we connect these surprising correlations to the intrinsic spin-density entanglement of the Fermi sea. The thermal wavelength supplies a cutoff scale at finite temperatures beyond which correlations are exponentially suppressed. We present data for the frequency dependent retarded spin-spin susceptibility and use the results to calculate the real-time response of a weak perturbation in linear response: within the spatial resolution no response outside of the light cone is found.