Accumulation of scale-free localized states induced by local non-Hermiticity

Systems with local non-Hermiticity are beyond the scope of both Bloch and non-Bloch band descriptions. Here, the authors establish a new paradigm for such systems: the emergence of scale-free localized states induced by local non-Hermiticity. They demonstrate that the scale-free localization is a generic phenomenon, regardless of the parity-time symmetry, the eigenstates' coalescence, or even the incommensurate disorder. The results also indicate that the bulk properties of the original Hermitian systems can be globally reshaped by local non-Hermiticity.