General theory for infernal points in non-Hermitian systems

The coalescence of eigenstates is a unique phenomena in non-Hermitian\nsystems. Remarkably, it has been noticed in some non-Hermitian systems under\nopen boundary conditions that the whole set of eigenstates can coalesce to only\na few eigenstates. In the parameter space, the point at which such a\ncoalescence of macroscopic eigenstates occurs is dubbed as an infernal point.\nIn this paper, based on the non-Bloch band theory and amoeba formulation, we\nestablish the criteria for the presence of infernal points in one-dimensional\nand higher dimensional open-boundary non-Hermitian systems. In addition, we\nfind an explanation of the extreme localization of the wave functions and\nunveil the mechanism for the coalescence of enormous eigenstates at the\ninfernal points. Our work provides a general theory for infernal points in\nopen-boundary non-Hermitian systems in arbitrary dimensions, and hence paves\nthe way to study the intriguing infernal points systematically.\n