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Interaction-driven phase transition in one dimensional mirror-symmetry protected topological insulator
by Devendra Singh Bhakuni, Amrita Ghosh, Eytan Grosfeld
This Submission thread is now published as
|Authors (as registered SciPost users):
|Devendra Singh Bhakuni · Amrita Ghosh · Eytan Grosfeld
Topological crystalline insulators are phases of matter where the crystalline symmetries solely protect the topology. In this work, we explore the effect of many-body interactions in a subclass of topological crystalline insulators, namely the mirror-symmetry protected topological crystalline insulator. Employing a prototypical mirror-symmetric quasi-one-dimensional model, we demonstrate the emergence of a mirror-symmetry protected topological phase and its robustness in the presence of short-range interactions. When longer-range interactions are introduced, we find an interaction-induced topological phase transition between the mirror-symmetry protected topological order and a trivial charge density wave. The results are obtained using density-matrix renormalization group and quantum Monte-Carlo simulations in applicable limits.
Published as SciPost Phys. Core 5, 048 (2022)
Author comments upon resubmission
We would like to thank you and the Referees for their positive evaluation and suggestions.
We want to highlight that our work provides a simple one-dimensional model that admits a topological phase that is protected by time-reversal symmetry and mirror-symmetry alone, amenable to exploration in the presence of many-body interactions. In the revised manuscript, we have demonstrated an interaction-induced transition from a topological mirror-symmetry protected dimer-insulating phase to a topologically trivial charge density wave phase. To the best of our knowledge, this is the first time that such an interaction-induced topological phase transition is shown between a fermionic 1d crystalline topological phase and a charge-density wave. Thus we feel that the work is an important contribution to the scientific community and has the scope for greater exploration in the future, for example with other lattice symmetries or with additional types of interactions.
We have revised our manuscript according to the suggestions of the referees. We also wanted to mention that symmetry-protected topological phases in one dimension are sometimes referred to as symmetry-obstructed atomic insulators as pointed out by Referee 1 and 3. While we prefer to go with the also prevalent nomenclature of topological insulators, we have added a paragraph to the discussion that highlights this point. Below we provide a point-by-point response to the questions raised by the Referees.
We thank you for your consideration and look forward to hearing back from you.
Devendra Singh Bhakuni, Amrita Ghosh, Eytan Grosfeld
List of changes
1. We modified the abstract, the introduction and conclusions to highlight the motivation for the paper in terms of the effect of interactions on mirror-symmetry-protected 1d topological phases. In particular, we added a treatment of NNNN interactions which can drive a phase transition at critical strength. In light of that, we also changed the title of the paper to reflect the stronger focus on interactions.
2. In the new Fig 7c and 7d we report the topological invariant in interacting cases.
3. In Fig. 8 and in the related discussion on pages 6-7 we demonstrate a phase transition that occurs at a critical strength of NNNN interactions using the entanglement entropy. New figures and additional discussion in the appendix describe the changes in the order parameters as a function of the strength of NNNN interactions.
Submission & Refereeing History
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Reports on this Submission
Clear motivation missing
Even in the revised version, I do not see the motivation to study the details of a toy model. In my view, it makes sense to study a toy model if it is representative of a larger class of models (corresponding to the given topological phase). Unfortunately, this work does not offer any new results that apply to the whole class of mirror-symmetric topological phases.
Report 1 by Alexander Lau on 2022-7-20 (Invited Report)
- Cite as: Alexander Lau, Report on arXiv:2202.07436v2, delivered 2022-07-20, doi: 10.21468/SciPost.Report.5422
1 - interesting study of a topological model linking non-interacting topology with interaction physics
2 - the paper has a clear structure and reads nicely
3 - the calculations are sound and the results seem correct overall
4 - the manuscript provides all necessary details to understand the research carried out and the results
5 - provides an intuitive picture based on the formation of dimers to understand the numerical results, in particular the robustness of the topological phases in the presence of interactions
6 - finds a transition from a topological dimer insulator to a trivial charge-density-wave insulator for longer-range interactions
The authors have responded to all of my concerns and suggestions and have incorporated them in the manuscript. In particular, my concerns regarding the mirror symmetry and the introduction of the topological invariant have been clarified sufficiently. One of my comments has also motivated the authors to add a new and interesting aspect to their work, namely that longer-range hopping (NNNN) leads to a phase transition from the topological dimer state to a trivial charge-density-wave state. They have also shifted the focus of their work to this aspect, which strengthens the manuscript, in my opinion.
I am satisfied with the revised manuscript and believe that it satisfies all general acceptance criteria of SciPost Physics. Moreover, I also believe that this work has the potential to trigger more follow-up work exploring similar interaction effects and phase transitions involving other crystalline topological phases (expectation criterion no. 3). I therefore recommend publication in SciPost Physics.
1 - Typo in the new paragraph at the end of Appendix A: “Concomitantly, the structure factor S(π/2) increases from a value close to 0.3125 to a value close to 0.0625.” From Fig. 10 and the text, it looks as if the V3=0 value should rather be 0.03125. The same typo is repeated a bit later in the same paragraph.