A numerical renormalization group approach to non-equilibrium Green functions for quantum impurity models

We present a method for the calculation of dynamical correlation functions of quantum impurity systems out of equilibrium using Wilson's numerical renormalization group (NRG). Our formulation is based on a complete basis set of the Wilson chain and embeds the recently derived algorithm for equilibrium spectral functions. Our method fulfils the spectral weight conserving sum-rule exactly by construction. A local Coulomb repulsion U > 0 is switched on at t = 0, and the asymptotic steady-state spectral functions are obtained for various values of U as well as magnetic field strength H and temperature T. These benchmark tests show excellent agreement between the time-evolved and the directly calculated equilibrium NRG spectra for finite U. This method could be used for calculating steady-state non-equilibrium spectral functions at finite bias through interacting nanodevices.