Non-Hermitian Hamiltonians, as effective models, capture phenomena such as energy dissipation and nonunitary evolution in open quantum systems. New phases and phenomena appear that are not present in their Hermitian counterparts. Such a Hamiltonian, the non-Hermitian Kondo model, has been used to describe inelastic scattering between mobile and confined atoms in an optical lattice [M. Nakagawa, N. Kawakami, and M. Ueda, Phys. Rev. Lett. 121, 203001 (2018)]. Using a combination of Bethe ansatz and perturbative calculation, the authors argued that this model has two distinct phases: the Kondo and the non-Kondo phases, where the impurity is screened and unscreened, respectively. We show, however, that a novel phase termed $\widetilde{YSR}$ emerges between the Kondo and unscreened phases. Characterized by two RG invariants: a generalized Kondo temperature ($T_K$) and a loss strength parameter ($\alpha$), the system exhibits three distinct phases. In the increasing order of losses, they are: the Kondo phase ($0<\alpha <\pi /2$), the $\widetilde{YSR}$ phase ($\pi /2<\alpha <3\pi /2$), and the local moment phase ($\alpha >3\pi /2$). Notably, phase transition driven by dissipation occurs across $\alpha =\pi /2$, where both energetics and different timescales associated with loss play roles.

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• Kondo effect
• Non-Hermitian systems
• Bethe ansatz