Towards realistic simulations of strongly correlated open quantum systems in steady-state

We discuss the applicability of theoretical Green's function methods to open quantum systems out of equilibrium, in particular, to single molecule junctions. Two characteristic energy scales governing the physics are many-body interactions within junctions and molecule–contacts couplings. Both weak interactions and weak coupling cases can be treated within diagrammatic expansions. However, lacking small parameter, the intermediate regime, where these two scales are comparable, can mostly be treated efficiently within the nonequilibrium dual approaches. We discuss the recently developed auxiliary quantum master equation dual-fermion and dual-boson approaches. Applications of both approaches in realistic simulations are limited by heavy numerical cost, which grows exponentially with system size when solving the auxiliary quantum master equation. Therefore, we explore the possibility of employing the flow equation renormalization group and low-order many-body Green's function techniques as inexpensive solvers capable of providing single- and two-particle Green's functions of the auxiliary problem. This will be a valuable addition to the theoretical toolbox by itself and as a part of a divide-and-conquer type of approach to study the response of strongly correlated open quantum systems to external perturbations in the field of spintronics, optoelectronics, and energy harvesting.