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Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain
by He-Ran Wang, Bo Li, Fei Song, Zhong Wang
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|Authors (as registered SciPost users):||Heran Wang|
|Preprint Link:||https://arxiv.org/abs/2301.11896v2 (pdf)|
|Date submitted:||2023-08-24 04:32|
|Submitted by:||Wang, Heran|
|Submitted to:||SciPost Physics|
We study the open XXZ spin chain with a PT-symmetric non-Hermitian boundary field. We find an interaction-induced scale-free non-Hermitian skin effect by using the coordinate Bethe ansatz. The steady state and the ground state in the PT broken phase are constructed, and the formulas of their eigen-energies in the thermodynamic limit are obtained. The differences between the many-body scale-free states and the boundary string states are explored, and the transition between the two at isotropic point is investigated. We also discuss an experimental scheme to verify our results.
Author comments upon resubmission
Thank you very much for handling our manuscript. We have revised our manuscript in response to the insightful feedback provided by the referees. Through careful consideration, we have carefully addressed all the comments and suggestions raised during the review. We believe that the revised manuscript is now suitable for publication.
List of changes
1) We have cited Ref.  as an example of spin chains with diagonal boundary field, as suggested by referee 2.
2) In the second paragraph of the Introduction, we have added some sentences to discuss the previous literature on exact solutions of open spin chains with arbitrary boundary fields, where related references [26-28] are included.
3) Also in the second paragraph of the Introduction, we have added a sentence on the non-unitary CFT, together with Ref. [32,33]. The Ref.  is recommended by the referee 2.
4) In the third paragraph of the Introduction, we have cited Ref. [49,50] about exactly solvable models with bulk non-Hermiticity, and compared them with our work.
5) We have changed the term "imaginary Bethe equation" to the "imaginary Fredholm equation", and demonstrate it in the note Ref. .
6) In page 5 We have cited Ref. , and modified our expression to emphasize that we obtained the closed-form expression for the complex momentum distribution.
7) In the Sec. 3.2, below Eq. (11) we have added a paragraph to discuss the effect of adding integrability terms on the two-magnon spectrum.
8) We have conducted numerical calculations to solve the discrete Bethe equations at Δ=-0.8, and added the new data in Fig. 6. We have also added an appendix to demonstrate our method of calculations. The calculations are independent of the analytical solutions and the exact diagonalization.
9) We have added a paragraph at the end of Sec. 5 to discuss Fig. 8 thoroughly.
Submission & Refereeing History
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- Report 2 submitted on 2023-10-07 11:41 by Anonymous
- Report 1 submitted on 2023-09-25 14:14 by Anonymous