Critical behavior of Non-Hermitian Kondo effect in a pseudogap system

A combined study of non-Hermitian physics and strong correlations can yield numerous intriguing effects. Authors of a previous study on the non-Hermitian Kondo model in the ultracold atoms reported the reversion of the renormalization group (RG) flow. In this paper, we investigate the non-Hermitian Kondo effect in the system with a specific form of density of states $\rho (\omega) \sim |\omega|^{r}(r>0)$, known as the pseudogap system. We find that, for $r<\frac{1}{2}$, our results from perturbative RG are consistent with those of the Hermitian pseudogap Kondo effect. For $r=\frac{1}{2}$, a fixed point with the reversion property emerges in the RG flow. For $r>\frac{1}{2}$, an unstable fixed point appears in the complex plane of the parameter space. Furthermore, through the large-$N$ expansion, we validate the RG results for $r < \frac{1}{2}$, finding that the self-consistent equations have non-trivial solutions in a specific region of the complex plane of the parameter space.