Symmetry-protected exceptional rings in two-dimensional correlated systems with chiral symmetry

Emergence of exceptional points in two dimensions is one of the remarkable phenomena in non-Hermitian systems. We here elucidate the impacts of symmetry on the non-Hermitian physics. Specifically, we analyze chiral symmetric correlated systems in equilibrium where the non-Hermitian phenomena are induced by the finite lifetime of quasiparticles. Intriguingly, our analysis reveals that the combination of symmetry and non-Hermiticity results in topological degeneracies of energy bands which we call symmetry-protected exceptional rings (SPERs). We observe the emergence of SPERs by analyzing a non-Hermitian Dirac Hamiltonian. Furthermore, by employing the dynamical mean-field theory, we demonstrate the emergence of SPERs in a correlated honeycomb lattice model whose single-particle spectrum is described by a non-Hermitian Dirac Hamiltonian. We uncover that the SPERs survive even beyond the non-Hermitian Dirac Hamiltonian, which is related to a zeroth Chern number. The argument of symmetry protection also holds for three dimensions, elucidating the presence of a symmetry-protected exceptional torus.

Figure 1

Sketch of the honeycomb lattice. Blue (red) spheres denote the $A\left(B\right)$ sublattice, respectively. ${\mathit{a}}_1,{\mathit{a}}_2$, and ${\mathit{a}}_3$ denote vectors connecting neighboring sites which are defined as ${\mathit{a}}_1:=(\sqrt{3},1)/2,{\mathit{a}}_2:=(-\sqrt{3},1)/2$, and ${\mathit{a}}_3:=(0,-1)$. Gray (brown) bonds represent hopping $t\left(rt\right)$, respectively.

Figure 2

Momentum-revolved spectral weight for several values of temperature at $(U_A,U_B)=(10t,5t)$. White lines illustrate the hexagonal BZ. The effective Hamiltonian becomes defective on the green lines. Panels (a), (b), and (c) are the data for $r=1$ where the system has two Dirac cones, while panel (d) shows the data for $r=2.2$ where the Dirac cones are absent. The inset of panel (d) shows the magnification of the data around the BZ boundary.

Figure 3

Color map of the zeroth Chern number for $t=r=d=1$. Panel (a) [(b)] shows the data for $V=0[V=0.3t]$. Here, the Chern number at each point is indicated by a number enclosed with a box. SPERs are represented with black lines. The black hexagon illustrates the BZ. Here, we shift origin of the Chern number so that it takes “0” when the $4\times 4$ matrix $H_{+}\left(\mathit{k}\right)$ has two occupied states.