Non-Hermitian Kondo Effect in Ultracold Alkaline-Earth Atoms

We investigate the Kondo effect in an open quantum system, motivated by recent experiments with ultracold alkaline-earth(-like) atoms. Because of inelastic collisions and the associated atom losses, this system is described by a complex-valued Kondo interaction and provides a non-Hermitian extension of the Kondo problem. We show that the non-Hermiticity induces anomalous reversion of renormalization-group flows which violate the $g$ theorem due to nonunitarity and produce a quantum phase transition unique to non-Hermiticity. Furthermore, we exactly solve the non-Hermitian Kondo Hamiltonian using a generalized Bethe ansatz method and find the critical line consistent with the renormalization-group flow.

Figure 1

RG flow of the non-Hermitian Kondo model (3) up to the 2-loop order. The blue curve shows the critical line obtained from the analytical solution of the RG equation [Eq. (S7) in Supplemental Material 35], and the red curve is the critical line obtained from the Bethe-ansatz solution [Eq. (16)].

Figure 2

Spin rapidities obtained from the numerical solutions of the Bethe equations (9) for the total number of particles $N=60$, 100, 200 and the number of spin-down particles $M=N/2$. The Kondo coupling is set to be ${\rho }_{0}J=-0.3+0.1i$.