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

The non-Hermitian skin effect (NHSE), an anomalous localization behavior of bulk states, is an inherently non-Hermitian phenomenon, which cannot find a counterpart in Hermitian systems. However, the fragility of the NHSE has been revealed recently, such as the boundary sensitivity, and it has stimulated many studies 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 in the thermodynamic limit. Distinct from previous studies, our proposed criterion only relies on analyzing the symmetry of the system, omitting 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 exact diagonalization numerical studies. Our results reveal a profound connection between the symmetry and the fate of the NHSE.