Kondo breakdown induced by the non-Hermitian complex hybridization

Abstract

Recently, a non-Hermitian Anderson impurity model with one-body loss has been studied in [Phys. Rev. B 111, 125157 (2025)}], and it has been demonstrated that the renormalization effect generated by strong correlations counterintuitively changes the nature of dissipation into an emergent many-body dissipation that causes a Kondo breakdown. In a closely related context, it is also known that two-body loss in a non-Hermitian Kondo model triggers the Kondo breakdown. To elucidate the essence of these phenomena, we study the Anderson impurity model with a non-Hermitian complex hybridization as an effective model that provides a simple understanding of the Kondo breakdown. Using the slave-boson mean-field theory, we show that this model can explain the Kondo breakdown with a single complex parameter. Furthermore, we provide the exact Bethe ansatz solutions that support the results obtained by the slave-boson mean-field theory. Finally, we point out that the Lehmann representation for the non-Hermitian Green function cannot be obtained by the analytic continuation to the complex energy upon the Kondo breakdown, where the analyticity of the non-Hermitian Green function in the half-complex-$ω$ plane no longer holds.

Figures (4)

• Figure 1: (a) Real and (b) imaginary parts of $\tilde{\Delta}$ as a function of the imaginary coupling $V$. The parameters are set to $D=1$ and $V_0=0.45$.
• Figure 2: Numerical solutions of the SCEs \ref{['eq_self']}. (a), (b) Resonance width for the retarded and the advanced Green functions. (c), (d) Imaginary and real parts of the renormalized complex impurity level (the imaginary part is reversed for convenience). (e), (f) Real and imaginary parts of the renormalized complex hybridization. (g), (h) Peak position for the retarded and the advanced Green functions. For the deep impurity level $E_d$, we see in (a) and (b) the suppression of the Kondo effect characterized by the decrease of the renormalized resonance width. In (c), we find that $-\mathrm{Im}\tilde{\lambda}$ is almost pinned to zero for the deep impurity level $E_d$, which highlights that the renormalized hybridization $\Delta_b$ is the only renormalized complex parameter that describes the Kondo breakdown. The parameters are set to the same values as those in Fig. \ref{['fig_DeltaVtilde']}.
• Figure 3: Comparison between $T_K^\mathrm{NH}$ analytically obtained from Eq. \ref{['eq_NHTK']} (dashed curves) and the resonance width $\Delta_b^\mathrm{Re}-\mathrm{Im}\tilde{\lambda}$ (solid curves) obtained from the numerical calculation of the SCEs \ref{['eq_self']}. For the deep impurity level $E_d$, both results agree well. The parameters are set to the same values as those in Fig. \ref{['fig_DeltaVtilde']}.
• Figure 4: Schematic illustration of the Kondo model implemented with ultracold atoms. In the case of alkaline-earth atoms, the ground state ${}^1S_0$ and the metastable state ${}^3P_0$ are trapped in a state-dependent optical lattice and serve as itinerant fermions and localized impurities, respectively. Interorbital spin-exchange interactions have been experimentally observed, where two-body loss is caused by inelastic collisions between the stable ${}^1S_0$ state and the metastable ${}^3P_0$ state Riegger18Ono21.