We discuss a particular source of error in the Numerical Renormalization Group (NRG) method for quantum impurity problems, which is related to a renormalization of impurity parameters due to the bath propagator. At any step of the NRG calculation, this renormalization is only partially taken into account, leading to systematic variation of the impurity parameters along the flow. This effect can cause qualitatively incorrect results when studying quantum critical phenomena, as it leads to an implicit variation of the phase transition's control parameter as function of the temperature and thus to an unphysical temperature dependence of the order-parameter mass. We demonstrate the mass-flow effect for bosonic impurity models with a power law bath spectrum, J(ω) ∝ ω s , namely the dissipative harmonic oscillator and the spin-boson model. We propose an extension of the NRG to correct the mass-flow error. Using this, we find unambiguous signatures of a Gaussian critical fixed point in the spin-boson model for s < 1/2, consistent with mean-field behavior as expected from quantum-to-classical mapping.

The time-dependent numerical renormalization-group approach (TD-NRG), originally devised for tracking the real-time dynamics of quantum-impurity systems following a single quantum quench, is extended to multiple switching events. This generalization of the TD-NRG encompasses the possibility of periodic switching, allowing for coherent control of strongly correlated systems by an external time-dependent field. To this end, we have embedded the TD-NRG in a hybrid framework that combines the outstanding capabilities of the numerical renormalization group to systematically construct the effective low-energy Hamiltonian of the system with the prowess of complementary approaches for calculating the real-time dynamics derived from this Hamiltonian. We demonstrate the power of our approach by hybridizing the TD-NRG with the Chebyshev expansion technique in order to investigate periodic switching in the interacting resonant-level model. Although the interacting model shares the same low-energy fixed point as its noninteracting counterpart, we surprisingly find the gradual emergence of damped oscillations as the interaction strength is increased. Focusing on a single quantum quench and using a strong-coupling analysis, we reveal the origin of these interaction-induced oscillations and provide an analytical estimate for their frequency. The latter agrees well with the numerical results.

A hybrid approach to nonequilibrium dynamics of quantum impurity systems is presented. The numerical renormalization group serves as a means to generate a suitable low-energy Hamiltonian, allowing for an accurate evaluation of the real-time dynamics of the problem up to exponentially long times using primarily the time-adaptive density-matrix renormalization group. We extract the decay time of the interaction-enhanced oscillations in the interacting resonant-level model and show their quadratic divergence with the interaction strength U . Our numerical analysis is in excellent agreement with analytic predictions based on an expansion in 1/U . Introduction. The description of strong electronic correlations far from thermal equilibrium poses an enormous theoretical challenge. At the root of the problem lies the nonequilibrium density operator which is not explicitly known in the presence of interactions. Of particular relevance are quench and driven dynamics realized in pump-probe experiments [1, 2], atomic traps [3,4], and nanodevices [5,6], where the full time evolution of the density operator should, in principle, be tracked.Quantum impurities systems (QIS) have regained considerable attention over the past 15 years due to the advent of carefully designed nanodevices. These generically consist of a few locally interacting degrees of freedom, typically a quantum dot, in contact with macroscopic leads. Since driven dynamics in nanodevices is of practical relevance to quantum computing and quantum control, considerable efforts were mounted in recent years toward devising approaches capable of treating the nonequilibrium state in QIS.Significant analytical progress in the calculation of real-time dynamics was achieved using different adaptations of perturbative renormalization-group ideas [7][8][9]. However, with the exception of Ref.[10], these are confined to the weak-coupling regime. Numerical methods, such as applications of the time-dependent densitymatrix renormalization group (TD-DMRG) [11,12] to QIS [13,14], the time-dependent numerical renormalization group (TD-NRG) [15], an iterated path-integral approach [16], and different continuous-time Monte Carlo simulations [17][18][19], are more flexible in the parameter regimes they can treat, but are either restricted to short time scales [13,14,[16][17][18][19] or susceptible to finite-size and discretization errors [13][14][15]. Indeed, finite-size representations are faced with an inherent difficulty of accurately representing the continuum limit even on intermediate time scales.In this paper, we report the extension of a recent hybrid approach [20] that overcomes some of the major ob-

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