  Non-Hermitian Hamiltonians capture several aspects of open quantum systems,
such as dissipation of energy and non-unitary evolution. An example is an
optical lattice where the inelastic scattering between the two orbital mobile
atoms in their ground state and the atom in a metastable excited state trapped
at a particular site and acting as an impurity, results in the two body losses.
It was shown in \cite{nakagawa2018non} that this effect is captured by the
non-Hermitian Kondo model. which was shown to exhibit two phases depending on
the strength of losses. When the losses are weak, the system exhibits the Kondo
phase and when the losses are stronger, the system was shown to exhibit the
unscreened phase where the Kondo effect ceases to exist, and the impurity is
left unscreened. We re-examined this model using the Bethe Ansatz and found
that in addition to the above two phases, the system exhibits a novel
$\widetilde{YSR}$ phase which is present between the Kondo and the unscreened
phases. The model is characterized by two renormalization group invariants, a
generalized Kondo temperature $T_K$ and a parameter `$\alpha$' that measures
the strength of the loss. The Kondo phase occurs when the losses are weak which
corresponds to $0<\alpha<\pi/2$. As $\alpha$ approaches $\pi/2$, the Kondo
cloud shrinks resulting in the formation of a single particle bound state which
screens the impurity in the ground state between $\pi/2<\alpha<\pi$. As
$\alpha$ increases, the impurity is unscreened in the ground state but can be
screened by the localized bound state for $\pi<\alpha<3\pi/2$. When
$\alpha>3\pi/2$, one enters the unscreened phase where the impurity cannot be
screened. We argue that in addition to the energetics, the system displays
different time scales associated with the losses across $\alpha=\pi/2$,
resulting in a phase transition driven by the dissipation in the system.
