Kondo effect in a non-Hermitian PT -symmetric Anderson model with Rashba spin-orbit coupling

The noninteracting and non-Hermitian, parity-time $(\mathcal{PT})$ symmetric Anderson model exhibits an exceptional point (EP) at a non-Hermitian coupling $g=1$, which remains unrenormalized in the presence of interactions [J. A. S. Louren\ifmmode \mbox{\c{c}}\else \c{c}\fi{}o et al., Phys. Rev. B 98, 085126 (2018)], where the EP was shown to coincide with the quantum critical point for Kondo destruction. In this work, we consider a quantum dot hybridizing with metallic leads having Rashba spin-orbit coupling $(\ensuremath{\lambda})$. We show that for a non-Hermitian hybridization, $\ensuremath{\lambda}$ can renormalize the exceptional point even in the noninteracting case, stabilizing $\mathcal{PT}$ symmetry beyond $g=1$. Through exact diagonalization of a zero-bandwidth, three-site model, we show that the quantum critical point and the exceptional point bifurcate, with the critical point for Kondo destruction at ${g}_{c}=1$, and the exceptional coupling being ${g}_{EP}>1$ for all $U\ensuremath{\ne}0$ and $\ensuremath{\lambda}\ensuremath{\ge}0;\ensuremath{\lambda}\ensuremath{\ne}U/2$. On the line $\ensuremath{\lambda}=U/2$, the critical point and the EP again coincide at ${g}_{c}={g}_{EP}=1$. The full model with finite-bandwidth leads is investigated through the slave-boson approach, using which we show that, in the strong-coupling regime, $\ensuremath{\lambda}$ and interactions cooperate in strongly reducing the critical point associated with Kondo destruction, below the $\ensuremath{\lambda}=0$ value.