Non-Hermitian Hamiltonians capture several aspects of open systems, systems in contact with their environment resulting in dissipation of energy and non-unitary evolution. The open Kondo system, consisting of an impurity spin attached with a complex coupling to a gas of electrons is an example where strong correlations interplay with dissipation effects. Solving the model exactly via the Bethe Ansatz, we show that the model is characterized by two renormalization group invariants, a generalized Kondo temperature and a parameter that measures the strength of the dissipation. We show that a rich phase diagram emerges as the strength of the dissipation varies. For weak dissipation we find the typical Kondo multi-particle screening of the impurity. As the dissipation increases the impurity screening mechanism changes, the Kondo cloud shrinks and the impurity is screened by a local bound state in a phase we call generalized YSR phase. Beyond this value the impurity is unscreened in the ground state though it may be screened at higher energy. For sufficiently strong dissipation it is in the local moment phase and cannot be screened at any energy scale. We argue that time evolution may drive the system across the phase transition point from the bound state to the unscreened state. I will also point out that a similar phase diagram emerges when the impurity is coupled to an s-wave superconductor with the condensate playing the role of the environment.
