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A detailed derivation of the recently proposed time-dependent numericalrenormalization-group (TD-NRG) approach to nonequilibrium dynamics in quantumimpurity systems is presented. We demonstrate that the method is suitable forfermionic as well as bosonic baths. A comparison with exact analytical resultsfor the charge relaxation in the resonant-level model and for dephasing in thespin-boson model establishes the accuracy of the method. The real-time dynamicsof a single spin coupled to both types of baths is investigated. We use theTD-NRG to calculate the spin relaxation and spin precession of a single Kondoimpurity. The short- and long-time dynamics is studied as a function oftemperature in the ferromagnetic and antiferromagnetic regimes. The short-timedynamics agrees very well with analytical results obtained at second order inthe exchange coupling $J$. In the ferromagnetic regime, the long-time spindecay is described by the scaling variable $x = 2\rho_F J(T) T t$. In theantiferromagnetic regime it is governed for $T < T_K$ by the Kondo time scale$1/T_K$. Here $\rho_F$ is the conduction-electron density of states and $T_K$is the Kondo temperature. Results for spin precession are obtained by rotatingthe external magnetic field from the x axis to the z axis.Comment: Revtex, 21 pages, 11 figures, 1 tabl

Spin precession and real-time dynamics in the Kondo model: Time-dependent numerical renormalization-group study