Out-of-equilibrium transport in the interacting resonant level model and comparison with the boundary sine-Gordon model.

We study the transport properties of the interacting resonant level model (IRLM) for arbitrary values of the interaction parameter $U$, and compare them with those of the Boundary sine-Gordon model (BSG), which are known analytically (Fendley, Ludwig and Saleur, 1995). While the IRLM and BSG models are expected not to be equivalent (except at two particular points: the free-fermion model and the self-dual point), we find that their $I$-$V$ curves are extraordinarily close, and can be distinguished only by a delicate analysis in the Infra Red (IR) regime. We also find that the shot noise in the two models is very similar for small enough values of $U$, but that marked differences appear for larger values of $Ugtrsim 5$. The numerical calculations of the IRLM are done using time-dependent Density Matrix renormalization Group (tDMRG) simulations. The shot noise is obtained by analyzing the second cumulant of the transferred charge, whose expectation value grows linearly with time, and extracting the corresponding rate from the simulations.