Lack of near-sightedness principle in non-Hermitian systems

1. The contents of the paper is well organised and clearly presented;
2. The research presented is timely and interesting;
3. The authors reveal that a non-Hermitian impurity results in a lack of the near-sightedness principle in otherwise Hermitian systems.

1. The observed effect seems somewhat straightforward.

The authors show that the near-sightedness principle breaks down in the presence of a non-Hermitian impurity. They demonstrate this effect for one- and two-dimensional systems both in the case of a non-Hermitian and Hermitian system. While the effect seems somewhat intuitive, I appreciate that the authors put this effect in the wider context of topological systems.

I have a few questions for the authors about their work:
1. The breakdown of the near-sightedness principle is demonstrated for the one-dimensional system in Fig. 1(a). To show the effect, the authors choose t_R= 0.9 and t_L = 1.1, i.e., the states in the model propagate to the left. The impurity is implemented in such a way that if h_imp ≠ 0 and >0, t_L becomes smaller and t_R becomes larger. In other words, at the impurity, the states would prefer to move in the opposite direction as compared to the rest of the chain. As such, it is not surprising to me that turning on h_imp > 0, one would at some point find an h_imp large enough for which all the states will accumulate at the impurity. Did the authors also check whether this effect takes place for h_imp < 0?
2. The text in the paper seems to imply that any non-Hermitian impurity would result in a breakdown of the near-sightedness principle. However, this is probably only the case for a non-reciprocal impurity like the one in red in Fig. 1(a). Is that indeed correct?

1. The on-site impurity seems to act as if it changes the boundary conditions if its value is large enough. To this end, the authors may wish to cite Roccati, Phys. Rev. A 104, 022215 (2021).
2. A transfer matrix setup with an impurity has also been studied in Dwivedi, Phys. Rev. B 97, 064201 (2018) for Hermitian systems. I believe this paper deserves a citation.

The description is clear enough.

The criticism to all papers on non-Hermitian skin effect is not well supported and unfair.

See attached.