Geometric meaning of high-order exceptional points in non-Hermitian Su-Schrieffer-Heeger model

Abstract We investigate the geometric meaning of high-order exceptional points (EPs) in non-Hermitian Su-Schrieffer-Heeger model. High-order EPs are highly associated with the non-Bloch parity-time (PT) symmetry, a novel type of PT symmetry caused by the non-Hermitian skin effect (NHSE). The bulk states arising from the NHSE possess higher-order EPs at the critical point of the non-Bloch PT phase transition. We also analyze the phase transition using the ratio of complex eigenenergies and employ saddle point theory to further clarify the geometric significance of higher-order EPs and non-Bloch PT phase transition. Finally, we generally prove that in an extended two-band non-Hermitian system, the values of generalized Brillouin zone at high-order EPs are zero or infinity. This work helps us further understand high-order EPs in nonreciprocal topological systems.