Non-Hermitian perspective of the band structure in heavy-fermion systems

We analyze a two-dimensional Kondo lattice model with special emphasis on non-Hermitian properties of the single-particle spectrum, following a recent proposal by Kozii and Fu. Our analysis based on the dynamical mean-field theory elucidates that the single-particle spectral weight shows the exceptional points (EPs). Correspondingly, the spectral weight exhibits the band touching, resulting in a structure similar to the Fermi arc. Furthermore, we find an intriguing phenomenon arising from the periodicity of the lattice. The EPs generated by two distinct Dirac points merge and change into a hybrid point, which vanishes as the exchange interaction is increased. Accordingly, the paramagnetic phase in the low-temperature region shows a significant difference from noninteracting fermions: the imaginary part of the self-energy yields the Fermi loop without any defective points.

Figure 1

The self-energy of the single-particle Green's function for several values of exchange interaction $J$: (a) the real part; (b) the imaginary part. As the interaction $J$ is increased, the Kondo effect is enhanced, which results in strong renormalization observed in (a) and a peak in the imaginary part around $\omega \sim 0$ as observed in (b).

Figure 2

Momentum-resolved spectral function for a given frequency ${\omega }_0$. In (a), we plot the spectral function by setting the imaginary part of the self-energy to zero. We note that the spectral function is symmetric under the transformations, $(k_x,k_y)\to (-k_x,k_y)$ and $(k_x,k_y)\to (k_x,-k_y)$. Because of the imaginary part of the self-energy, the effective Hamiltonian (5b) becomes defective at $(k_{0x},k_{0y})=(0.93,2.71)$, which is denoted as a green dot in (b).

Figure 3

(a) Local density of states for $J=1.8t$. The dashed lines represent the data obtained by setting $\mathrm{Im}{\mathrm{\Sigma }}_b^R\left(\omega \right)=0$. The local density of states is enhanced by the imaginary part of the self-energy, which induces the Fermi arc observed for the momentum resolved spectral functions. (b) Color map of ${\mathrm{\Delta }}_c^2$. The dashed white lines denote the branch cut. The white arrows point at EPs. The green line with arrows denotes the path of the integral of Eq. (8).

Figure 4

Momentum-resolved spectral function for a given frequency ${\omega }_0$. Because the conduction electrons are effectively decoupled, we can observe the peak at $k_y=\pi$ in (a), signaling the emergence of the Dirac point. In (b), the effective Hamiltonian is not defective in the entire BZ although the imaginary part of the self-energy show a sharp dip around $\omega =0$ [see Fig. 1].

Figure 5

Local density of states and the color map of ${\mathrm{\Delta }}_c^2$ for $J=2t$, which are plotted in a similar way to Fig. 3.

Figure 6

Phase diagram of the spin exchange interaction $J$ vs. the temperature $T$. The solid green line denotes the Neel temperature. The dashed blue line denotes the Kondo temperature, which is estimated from saturation of the singlet correlation between the conduction electron and the localized spin. The dashed horizontal line denotes the temperature $T=0.048t$. The EPs and the Fermi arc are observed above the Neel temperature.