Quantum quench dynamics in quantum impurity models using the auxiliary field approach

We study the transient dynamics of the interacting Anderson impurity model after a quantum quench. Specifically, we use the auxiliary field approach to calculate the time-dependence of the real-frequency impurity spectral function due to a sudden change in the impurity level energy or interaction strength. The auxiliary field approach [1] was recently introduced in the context of equilibrium dynamical mean field theory for the Hubbard model, and involves mapping the exact interaction self-energy to an effective non-interacting auxiliary system living in an enlarged Hilbert space. Here we generalize the method to a nonequilibrium setting which, although approximate, provides physical insights and qualitatively correct results at low computational cost. The structure of the auxiliary field is determined exactly from the equilibrium self-energy for the pre- and post-quench Hamiltonians (obtained here using the numerical renormalization group). The quench in the physical system is then assumed to correspond to a quench in the auxiliary field configuration, and the effect on the impurity dynamics is found using nonequilibrium Green's function methods. An immediate implication of the mapping is a light-cone effect, which means that low-energy spectral features take longer to relax than high-energy features. We discuss the possible consequences of this for quenching across the Mott transition in the Hubbard model, where nonequilibrium quasistationary states emerge at intermediate timescales.