  We present the real-time renormalization group (RTRG) method as a method to
describe the stationary state current through generic multi-level quantum dots
with a complex setup in nonequilibrium. The employed approach consists of a
very rudiment approximation for the RG equations which neglects all vertex
corrections while it provides a means to compute the effective dot Liouvillian
self-consistently. Being based on a weak-coupling expansion in the tunneling
between dot and reservoirs, the RTRG approach turns out to reliably describe
charge fluctuations in and out of equilibrium for arbitrary coupling strength,
even at zero temperature. We confirm this in the linear response regime with a
benchmark against highly-accurate numerically renormalization group data in the
exemplary case of three-level quantum dots. For small to intermediate bias
voltages and weak Coulomb interactions, we find an excellent agreement between
RTRG and functional renormalization group data, which can be expected to be
accurate in this regime. As a consequence, we advertise the presented RTRG
approach as an efficient and versatile tool to describe charge fluctuations
theoretically in quantum dot systems.
