Anomalous symmetry protected blockade of skin effect in one-dimensional non-Hermitian lattice systems

Abstract: The non-Hermitian skin effect (NHSE), an anomalous localization behavior of the bulk states, is an inherently non-Hermitian phenomenon, which can not find a counterpart in Hermitian systems. However, the fragility of NHSE has been revealed recently, such as the boundary sensitivity, and it stimulates a lot of studies on discussing the fate of that. Here we present a theorem which shows that the combined spatial reflection symmetry can be considered as a criterion in one-dimensional non-Hermitian systems to determine whether the NHSE can exist or not. Distinct from previous studies, our proposed criterion only relies on analyzing the symmetry of the system, freeing out other requirements, such as the information of the energy spectrum. Furthermore, by taking the non-Hermitian Kitaev chain as an example, we verify our theorem through both a mathematical proof via the non-Bloch band theory and the exact diagonalization numerical studies. Our results reveal a profound connection between the symmetry and the fate of NHSE.