SciPost Submission Page
Hidden dualities in 1D quasiperiodic lattice models
by Miguel Gonçalves, Bruno Amorim, Eduardo V. Castro, Pedro Ribeiro
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Miguel Gonçalves · Pedro Ribeiro |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2103.03895v4 (pdf) |
| Date accepted: | 2022-07-05 |
| Date submitted: | 2022-06-07 15:57 |
| Submitted by: | Gonçalves, Miguel |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We find that quasiperiodicity-induced transitions between extended and localized phases in generic 1D systems are associated with hidden dualities that generalize the well-known duality of the Aubry-Andr\'e model. These spectral and eigenstate dualities are locally defined near the transition and can, in many cases, be explicitly constructed by considering relatively small commensurate approximants. The construction relies on auxiliary 2D Fermi surfaces obtained as functions of the phase-twisting boundary conditions and of the phase-shifting real-space structure. We show that, around the critical point of the limiting quasiperiodic system, the auxiliary Fermi surface of a high-enough-order approximant converges to a universal form. This allows us to devise a highly-accurate method to obtain mobility edges and duality transformations for generic 1D quasiperiodic systems through their commensurate approximants. To illustrate the power of this approach, we consider several previously studied systems, including generalized Aubry-Andr\'e models and coupled Moir\'e chains. Our findings bring a new perspective to examine quasiperiodicity-induced extended-to-localized transitions in 1D, provide a working criterion for the appearance of mobility edges, and an explicit way to understand the properties of eigenstates close to and at the transition.
Author comments upon resubmission
Thank you very much for your time and consideration of our manuscript. We are grateful for the very positive Referee reports on our work and for the very useful suggestions and comments that were made by you and the Referees.
In our revised manuscript, we have corrected all the typos that you and the Referees noticed. We also tried to improve accessibility and readability of the manuscript. In particular, we added to each figure caption reminders of the model and parameters being studied in that figure, and added hyperlinks to the relevant equations where these were defined. We also specified the Appendix sections that we are referring to whenever they are mentioned in the main sections for a faster navigation throughout the manuscript.
On more specific details, regarding section II, we have both the "Aubry-André duality" and "General dualities" sub-sections.
In our responses to the Referee reports, we addressed all the points raised by the Referees and indicated the changes that we made in the manuscript regarding these questions, whenever applicable.
Yours sincerely,
Miguel Gonçalves
List of changes
- Added table of contents at the beginning of the manuscript;
- Corrected typos spotted by the Editor and the Referees and implemented their suggestions. In particular:
-- Added an inset to Fig.2(b) an example with results of the prediction of self-dual points through commensurate approximants having different unit cell sizes, in comparison with the estimation of the critical point through the inverse participation ratio for a large system size;
-- Added a dashed box around Figs.2(e,f) connecting them with Fig2.(d) to make it clear that the former were obtained for the model in the latter;
-- Clarified the purpose of the grey and magenta shaded regions in the caption of Fig.4;
-- Added to each figure caption reminders of the model and parameters being studied in that figure, and added hyperlinks to the relevant equations where these were defined;
-- Specified the Appendix sections that we are referring to whenever they are mentioned in the main sections, for a faster navigation throughout the manuscript.
- Added a discussion on some questions raised by in Referee report 2 to the "Discussion" section (paragraph "The scope of this work (...)");
- Added an Appendix (Appendix F).
Published as SciPost Phys. 13, 046 (2022)