SciPost Submission Page
Lack of near-sightedness principle in non-Hermitian systems
by Helene Spring, Viktor Könye, Anton R. Akhmerov, Ion Cosma Fulga
Submission summary
| Authors (as registered SciPost users): | Anton Akhmerov · Ion Cosma Fulga · Viktor Könye · Helene Spring |
| Submission information | |
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| Preprint Link: | scipost_202310_00002v1 (pdf) |
| Code repository: | https://doi.org/10.5281/zenodo.8204845 |
| Data repository: | https://doi.org/10.5281/zenodo.8204845 |
| Date submitted: | 2023-10-03 11:34 |
| Submitted by: | Spring, Helene |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The non-Hermitian skin effect is a phenomenon in which an extensive number of states accumulates at the boundaries of a system. It has been associated to nontrivial topology, with nonzero bulk invariants predicting its appearance and its position in real space. Here we demonstrate that the non-Hermitian skin effect is not a topological phenomenon in general: when translation symmetry is broken by a single non-Hermitian impurity, skin modes are depleted at the boundary and accumulate at the impurity site, without changing any bulk invariant. This may occur even for a fully Hermitian bulk.
Current status:
Reports on this Submission
Strengths
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.
Weaknesses
1. The observed effect seems somewhat straightforward.
Report
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?
Requested changes
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.
Strengths
The description is clear enough.
Weaknesses
The criticism to all papers on non-Hermitian skin effect is not well supported and unfair.
Report
See attached.