We present a general scheme to map correlated nonequilibrium quantum impurity problems onto an auxiliary open quantum system of small size. The infinite fermionic reservoirs of the original system are thereby replaced by a small number NB of noninteracting auxiliary bath sites whose dynamics is described by a Lindblad equation. Due to the presence of the intermediate bath sites, the overall dynamics acting on the impurity site is non-Markovian.With the help of an optimization scheme for the auxiliary Lindblad parameters, an accurate mapping is achieved, which becomes exponentially exact upon increasing NB. The basic idea for this scheme was presented previously in the context of nonequilibrium dynamical mean field theory. In successive works on improved manybody solution strategies for the auxiliary Lindblad equation, such as Lanczos exact diagonalization or matrix product states, we applied the approach to study the nonequilibrium Kondo regime.In the present paper, we address in detail the mapping procedure itself, rather than the manybody solution. In particular, we investigate the effects of the geometry of the auxiliary system on the accuracy of the mapping for given NB. Specifically, we present a detailed convergence study for five different geometries which, besides being of practical utility, reveals important insights into the underlying mechanisms of the mapping. For setups with onsite or nearest-neighbor Lindblad parameters we find that a representation adopting two separate bath chains is by far more accurate with respect to other choices based on a single chain or a commonly used star geometry. A significant improvement is obtained by allowing for long-ranged and complex Lindblad parameters. These results can be of great value when studying Lindblad-type approaches to correlated systems.

We study a simple model of photovoltaic energy harvesting across a Mott insulating gap consisting of a correlated layer connected to two metallic leads held at different chemical potentials. We address in particular the issue of impact ionization, whereby a particle photoexcited to the high-energy part of the upper Hubbard band uses its extra energy to produce a second particle-hole excitation. We find a drastic increase of the photocurrent upon entering the frequency regime where impact ionization is possible. At large values of the Mott gap, where impact ionization is energetically not allowed, we observe a suppression of the current and a piling up of charge in the high-energy part of the upper Hubbard band.Our study is based on a Floquet dynamical mean field theory treatment of the steady state with the so-called auxiliary master equation approach as impurity solver. We verify that an additional approximation, taking the self-energy diagonal in the Floquet indices, is appropriate for the parameter range we are considering.

We study equilibrium and nonequilibrium properties of the single-impurity Anderson model with a power-law pseudogap in the density of states. In equilibrium, the model is known to display a quantum phase transition from a generalized Kondo to a local moment phase. In the present work, we focus on the extension of these phases beyond equilibrium, i.e. under the influence of a bias voltage. Within the auxiliary master equation approach combined with a scheme based on matrix product states (MPS) we are able to directly address the current-carrying steady state. Starting with the equilibrium situation, we first corroborate our results by comparing with a direct numerical evaluation of ground state spectral properties of the system by MPS. Here, a scheme to locate the phase boundary by extrapolating the power-law exponent of the self energy produces a very good agreement with previous results obtained by the numerical renormalization group. Our nonequilibrium study as a function of the applied bias voltage is then carried out for two points on either side of the phase boundary. In the Kondo regime the resonance in the spectral function is splitted as a function of the increasing bias voltage. The local moment regime, instead, displays a dip in the spectrum near the position of the chemical potentials. Similar features are observed in the corresponding self energies. The Kondo split peaks approximately obey a power-law behavior as a function of frequency, whose exponents depend only slightly on voltage. Finally, the differential conductance in the Kondo regime shows a peculiar maximum at finite voltages, whose height, however, is below the accuracy level.

We address the steady-state behavior of a system consisting of several correlated monoatomic layers sandwiched between two metallic leads under the influence of a bias voltage. In particular, we investigate the interplay of the local Hubbard and the long-range Coulomb interaction on the charge redistribution at the interface, in the paramagnetic regime of the system. We provide a detailed study of the importance of the various system parameters, like Hubbard U , lead-correlated region coupling strength, and the applied voltage on the charge distribution in the correlated region and in the adjacent parts of the leads. In addition, we also present results for the steady-state current density and double occupancies. Our results indicate that, in a certain range of parameters, the charge on the two layers at the interface between the leads and the correlated region display opposite signs producing a dipolelike layer at the interface. Our results are obtained within nonequilibrium (steady-state) real-space dynamical mean-field theory (R-DMFT), with a self-consistent treatment of the long-range part of the Coulomb interaction by means of the Poisson equation. The latter is solved by the Newton-Raphson method and we find that this significantly reduces the computational cost compared to existing treatment. As impurity solver for R-DMFT we use the auxiliary master equation approach (AMEA), which addresses the impurity problem within a finite auxiliary system coupled to Markovian environments.

We present further developments of the auxiliary master equation approach (AMEA), a numerical method to simulate many-body quantum systems in as well as out of equilibrium, and apply it to the Interacting Resonant Level Model (IRLM) to benchmark the new developments. In particular, our results are obtained by employing the stochastic wave functions (SWF) method to solve the auxiliary open quantum system arising within AMEA. This development allows to reach extremely low walltimes for the calculation of correlation functions with respect to previous implementations of AMEA. An additional significant improvement is obtained by extrapolating a series of results obtained by increasing the number of auxiliary bath sites, NB, used within the auxiliary open quantum system formally to the limit of NB → ∞. Results for the current-voltage characteristics and for equilibrium correlation functions are compared with the one obtained by exact and matrix-product states based approaches.