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Lack of near-sightedness principle in non-Hermitian systems
by Helene Spring, Viktor Könye, Anton R. Akhmerov, Ion Cosma Fulga
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Anton Akhmerov · Ion Cosma Fulga · Viktor Könye · Helene Spring |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202310_00002v2 (pdf) |
| Code repository: | https://zenodo.org/records/8204845 |
| Data repository: | https://zenodo.org/records/8204845 |
| Date accepted: | 2024-11-12 |
| Date submitted: | 2024-08-15 12:41 |
| Submitted by: | Spring, Helene |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| 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 has weaker bulk-edge correspondence than topological insulators: 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. Similarly, a single non-Hermitian impurity may deplete the states from a region of Hermitian bulk.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We have now responded to the referees and attached a redlined version of the manuscript with marked changes compared to the previous submission to our responses.
We believe that we have addressed the main concerns expressed in report 5 by clarifying the manuscript and addressing some of the misunderstanding.
Best regards,
The authors
List of changes
Listed in full in the replies to referees of the first submission.
Published as SciPost Phys. 17, 153 (2024)
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2024-11-4 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202310_00002v2, delivered 2024-11-04, doi: 10.21468/SciPost.Report.10035
Report
I was asked for a quick comment on the dispute between the referee and the authors. My report is as follows:
The Referee Report #4 raises two issues with the manuscript. Firstly, it claims that the "near-sightedness principle" applies to (Hermitian) topological insulators only insofar as the bulk states are localized in real space. This, as the authors point out in their response, is not true, since it applies to band insulators where all the bulk-states are Bloch waves. Even for systems where the localization of all states is forbidden by topology (such as QHE), I would not expect disorder deep in the bulk to destroy the boundary signature without simultaneously destroying the bulk topology. Secondly, the referee uses a non-unitary gauge transformation on the Hatano-Nelson model to essentially arrive at the same result as the manuscript, namely, that a single impurity, if strong enough, can remove all localized modes from the boundary (as is usual for the non-Hermitian skin effect) and localize them on the impurity instead. This, as the authors state in their response, is an instance of their result, whose application is more transparent in general owing to its use of transfer matrices.
In my opinion, while one may certainly debate the centrality of a nearsigntedness principle to a topological insulator, I think the authors have certainly demonstrated that it does not apply to the non-Hermitian skin effect, and that the boundary modes arising from it act quite unlike the topological boundary modes of Hermitian topological insulators. In conclusion, I do not believe that Referee Report #4 provides sufficient grounds for rejection of this manuscript.
Recommendation
Publish (meets expectations and criteria for this Journal)
Report #1 by Anonymous (Referee 1) on 2024-9-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202310_00002v2, delivered 2024-09-08, doi: 10.21468/SciPost.Report.9726
Report
I am satisfied by the change in the abstract, but I am not satisfied by the authors' response to my argument of the imaginary gauge transformation. I did not mean an alternative proof. What I meant was that the present paper complicates a much simpler mathematical fact. I don't think the complication of introducing "impurity" has any physical insight into the phenomenon of non-Hermitian skin effect. I thereby still do not recommend its publication.
Recommendation
Reject
Author: Anton Akhmerov on 2024-09-09 [id 4749]
(in reply to Report 1 on 2024-09-08)We are happy that the referee is satisfied with the changes in the abstract. The referee also does not raise any further concerns about the contents of our manuscript, nor do they refute any of the points in our reply.
The referee's assessment of our point regarding the rescaling transformation ignores the explanation in our response. There we say that this rescaling transformation is only applicable to a specific model, while the transfer matrix lower bound applies to all tight-binding nonhermitian models.
The referee also does not substantiate their point about lacking physical insight or their evaluation of the significance of the manuscript as "low". As also confirmed by the other referee, our observation is new in the literature, and the potential breakdown of NHSE is a significant aspect of its analysis.
The referee also evaluates the validity of our manuscript as "low" without providing any support for this evaluation.
For the above reasons we consider the referee report subjective, and not supported by scientific arguments.