We provide an exact description of out-of-equilibrium fixed points in quantum impurity models, that is able to treat time-dependent forcing. Building on this, we then show that analytical out-ofequilibrium results, that exactly treat interactions, can be obtained in interacting quantum impurity models in their strong coupling regime, provided they are integrable at equilibrium and they are "super Fermi liquids", i.e. they only allow for integer charge hopping. For such systems we build an out-of-equilibrium strong coupling expansion, akin to a Sommerfeld expansion in interacting systems. We apply our approach to the Interacting Resonant Level model, and obtain the exact expansion around the low energy fixed point of the universal scaling function for the charge current as a function of voltage, temperature, and frequency, up to order seven.The study of nano structures forced out-of-equilibrium is a vivid field of research, driven amongst other things by long term efforts towards the miniaturization of electronics. Rapid progresses in the realization of engineered micrometric structures coupled to macroscopic electrodes (e.g. quantum dots [1, 2]), or of hybrid devices consisting of atoms or molecules embedded in circuits [3][4][5] demonstrate the possibility of "single electron" electronics [6, 7]. A theoretical understanding of the mechanisms governing transport in those systems is thus of crucial importance. Whereas linear response -when the voltage across the nanostructure goes to zero -boils down to equilibrium properties and is fairly well understood, nonlinear effects are significantly harder to predict: solving the out-of-equilibrium theory unfortunately turns out to be a considerable problem, mixing many-body aspects (interactions make it complicated) with the intrinsically open geometry of the out-of-equilibrium problem.Those systems are modeled by quantum impurity models (QIM), that consist in continua of electronic degrees of freedom representing the metallic electrodes (the baths) interacting with the nanostructure (the "impurity"). A generic feature of QIM at equilibrium is that the impurity/bath coupling, no matter how small, has drastic consequence on the groundstate of the system: impurity degrees of freedom hybridize with the bath, so that effectively some, or all, impurity degrees of freedom are swallowed by the baths. In the zero energy E → 0 (groundstate) limit, impurity degrees of freedom are strongly bound to the baths, so that is is often called a strong coupling (SC) fixed point (FP). This last term means that the system has scale invariance in this limit [8, 9], resulting in the fact that the SC-FP is essentially an homogenous (the impurity "disappears") and free theory. This has direct physical consequences: for example, for systems with a Fermi liquid SC-FP [10,11], hybridization results in a linear I(V ) characteristic at small voltage, with the conductivity G 0 = ∂I ∂V V=0being maximal at T = 0 and at the particle-hole symmetric point. A typical energy scale, called here the hybridiza...

In this paper we develop a method to describe perturbatively the entanglement entropy in a simple impurity model, the interacting resonant level model (IRLM), at low energy (i.e. in the strong coupling regime). We use integrability results for the Kondo model to describe the infra-red fixed point, conformal field theory techniques initially developped by Cardy and Calabrese and a quantization scheme that allows one to compute exactly Renyi entropies at arbitrary order in 1/Tb in principle, even when the system size or the temperature is finite. We show that those universal quantities at arbitrary interaction parameter in the strong coupling regime are very well approximated by the same quantities in the free fermion system in the case of attractive Coulomb interaction, whereas a strong dependence on the interaction appears in the case of repulsive interaction.