The one-electron energy spectrum of correlated electron systems is described by an effective non-Hermitian, dynamical quasi-particle Hamiltonian. Due to the presence of imaginary part of the self-energy (in another word, finite lifetime of the quasiparticles), the may exist so-called “exceptional points” (EPs) in the Brillouin zone, at which the effective Hamiltonian become non-diagonalizable. At these EPs, a topological invariant can be defined , and different EPs in the Brillouin zone might be connected by Bulk Fermi arcs. In two independent works published recently [2,3], the topology of the effective single-particle Hamiltonian derived from two-dimensional periodic Anderson model has been analyzed in depth. With properly chosen model parameters (in particular the hybridization parameters), the EPs and consequently the bulk Fermi arcs appear naturally in such models, which has significant implications for heavy-fermion systems. It has been further proposed that the temperature at which EPs appear around the Fermi energy is intimately related to the Kondo temperature . That is, the well-known crossover between localized and itinerant f electrons in Kondo systems is related to the emergence of EPs. In both works [2,3], the theoretical analysis is corroborated by numerical calculations utilizing dynamical mean-field theory.
Huitao Shen, Bo Zhen, and Liang Fu, "Topological Band Theory for Non-Hermitian Hamiltonians", Phys. Rev. Lett. 120, 146402 (2018).
Yoshihiro Michishita, Tsuneya Yoshida, and Robert Peters, "Relationship between exceptional points and the Kondo effect in f -electron materials", Phys. Rev. B 101, 085122 (2020).
Yuki Nagai, Yang Qi, Hiroki Isobe, Vladyslav Kozii, and Liang Fu, "DMFT Reveals the Non-Hermitian Topology and Fermi Arcs in Heavy-Fermion Systems", Phys. Rev. Lett. 125, 227204 (2020).