Quantum Magnetism in Wannier-Obstructed Mott Insulators

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In the present work the authors develop the methodical approach to derive the effective spin Hamiltonian from the Wannier functions in a Mott insulator, taking into account the Wannier-obstructed state. This leads to new channels of spin exchange. Finally, they are applied to a Kagome lattice.
The paper is clearly written and can be published in its present form.

Author Response

We sincerely appreciate the reviewer's accurate summary and the recommendation for publication of our paper.

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents a novel approach to understanding Mott physics in Wannier obstructed systems, including Chern insulators and fragile topological systems like twisted bilayer graphene. The authors introduce a method to construct trial nonorthogonal Wannier orbitals and systematically project the Hamiltonian to a nonorthogonal spin basis to study low-energy spin dynamics. The manuscript effectively demonstrates the potential for new channels to spin interactions, leading to rich magnetic phases in models carrying Chern bands and fragile topological bands.

The manuscript is well-structured and provides valuable insights into the magnetisms in Moiré superlattice systems and their relevance to Wannier obstructed bands. The authors effectively demonstrate the significance of their approach in shedding light on ferromagnetic hysteresis in certain systems, providing a strong foundation for further research in this area.

1. The main question addressed by the research is how to understand quantum magnetism in Mott insulators with Wannier obstructed bands. The authors aim to establish an effective spin model from the electron Hamiltonian using a diagrammatic approach and investigate the implications of nonorthogonal Mott basis on spin-exchange interactions.
 
2. The topic is highly original and relevant in the field, as it addresses a specific gap in our understanding of quantum magnetism in Mott insulators with Wannier obstructed bands. This is particularly important given the experimental observations of robust ferromagnetism in such systems.
 
3. The manuscript adds significant value to the subject area compared with other published material by introducing a systematic method to study low-energy spin dynamics in Wannier obstructed systems. It also provides insights into the potential for new channels of spin interactions, leading to rich magnetic phases in models carrying Chern bands and fragile topological bands.
 
4. Specific improvements that the authors should consider regarding the methodology include providing further details on the implementation of the diagrammatic approach and addressing potential limitations or assumptions in the model. Additionally, the authors should consider discussing potential experimental validations or predictions arising from their theoretical framework.
 
5. The conclusions presented in the manuscript are consistent with the evidence and arguments provided. They effectively address the main question posed by shedding light on quantum magnetism in Mott insulators with Wannier obstructed bands.
 
6. The references cited in the manuscript are appropriate and support the theoretical framework presented. However, the authors may consider including more recent publications over the past 3-5 years related to quantum magnetism in similar systems to ensure comprehensive coverage of the literature.
 
7. The tables and figures in the manuscript are clear and effectively support the presented findings. However, the authors should ensure that figures 3-6 are properly labeled and described to enhance clarity for readers.

Author Response

We are grateful for the thorough review and constructive suggestions. We appreciate the reviewer's overall positive evaluation. Below, we address each point raised:

1. Understanding Quantum Magnetism in Mott Insulators: We thank the reviewer for carefully reading our paper and summarizing our main goal accurately.

2. Originality and Relevance: We appreciate the recognition of the originality of our work and its relevance to current research gaps.

3. Value Addition to the Subject Area: We appreciate the recognition of the value of our approach.

4. Methodology Improvements: We have improved the appendix sections and added further details on the implementation of the diagrammatic approach to our manuscript, addressing potential limitations and assumptions more explicitly. We also expand our discussion to comment on more recent experimental systems like rhombohedral multilayer graphene and twisted transition metal dichalcogenides (TMD), thereby bridging the gap between theory and experiment.

5. Consistency of Conclusions: We are pleased that the conclusions were found to be consistent with the evidence provided. 

6. References Update: Following the recommendation, we have updated our references section to include more recent publications from the last 3 years. This ensures our literature review is up-to-date, providing a broader context for our research within the current scientific discourse.

7. Tables and Figures Clarity: We have carefully reviewed figures 3-6, improving their labeling and descriptions to enhance clarity and reader comprehension. This revision aims to ensure that our visual aids effectively complement and elucidate the textual content of our manuscript.

We hope that these revisions and clarifications address the points raised by the reviewer satisfactorily and further strengthen our manuscript. We are thankful for the opportunity to improve our work based on your valuable feedback.

Reviewer 3 Report

Comments and Suggestions for Authors

Manuscript number: crystals-2818266 Crystals MDPI (type of the paper: Article, Section: Crystal Engineering Special Issue: Two-Dimensional Materials: Synthesis, Property and Applications)

 

TITLE: Quantum Magnetism in Wannier-Obstructed Mott Insulators

 

AUTHORS: Xiaoyang Huang, Taige Wang, Shang Liu, Hong-Ye Hu, Yi-Zhuang You

 

 

The first review of the manuscript

 

 

Overall description of the manuscript

 

In the manuscript entitled “Quantum Magnetism in Wannier-Obstructed Mott Insulators” authored by Xiaoyang Huang, Taige Wang, Shang Liu, Hong-Ye Hu, Yi-Zhuang You, the authors present theoretical approach to deal with strong coupling limit of the extended Hubbard model. The approach is based on non-orthogonal Wannier orbitals with finite orbital overlap. After the detailed presentation of the method, the authors apply it to the problem on the Kagome lattice and to some effective spin models. The paper is very good study and could be interesting for scientist investigating strongly correlated systems.

 

 

The paper fits the journal scope more or less (the method is general one but it is used to analyze two dimensional case). The English language in the manuscript is good. The paper has 30 pages and includes 65 references (equivalent to 3 pages), and 10 figures (about 3 pages) – effectively about 23 pages of the main text. The diagrams (figures) are clear, they are essential and their captions are informative. The title clearly and concisely conveys the topic of the article. The abstract quite well describes the content of the manuscript. The findings look correctly. The discussion and conclusions are supported by the results.

 

In my opinion the manuscript can be published after introduction of some modification before the final publication according to the points mentioned below. I believe that suggested improvements can increase the readability and quality of the paper.

 

 

Some specific comments to the authors:

 

1) It would be good to contrast the presented findings (Section 5) with the results found by some other methods. The strongly correlated behavior has been investigated intensively in the last years in the systems with flat bands, particularly, in the kagome lattice systems. The other results are easy to find and discuss.

 

2) The extended Hubbard model and its limit has been extensively investigated in the context of the Mott transition and coexisting charge orders (see, e.g., Nat. Phys. 4, 932 (2008); Phys. Rev. B 82, 155102 (2010); Phys. Rev. Lett. 111, 126403 (2013); Phys. Rev. B 90, 195114 (2014); Phys. Rev. B 95, 125112 (2017); and reference therein). Maybe authors could extend the discussion in the introduction to cover also this context of their work.

 

 

To sum up, after these issues will be resolved, I strongly believe the submitted manuscript is suitable for publication in “Crystals” MDPI journal as an article in the special issue, however the authors should consider the points above. The topic of the paper, which is strongly associated with new methods in strongly correlated systems, attracts a lot of attention (because of their potential applications and new phenomena possible) and can be interesting for some groups of scientists.

Author Response

We thank the reviewer for the comprehensive review and constructive suggestions. We appreciate the reviewer's overall positive recommendation for publishing our work. Below, we address the comments point by point, detailing the modifications made to the manuscript in response.

1. Contrast with Other Methods (Section 5): 

   In response to the reviewer's suggestion for contrasting our findings with other methods, Section 5 has been updated to directly reference a spectrum of studies ([20,23,70–76]) that our phase diagram qualitatively aligns with. This section now succinctly discusses how our approach to the Hubbard model in topological bands complements and diverges from existing theoretical and numerical research.

   We have also clarified our examination of exotic phases within the spin model (Eq. 34), citing specific studies ([77–84]) that explore the potential for chiral and gapless spin liquid phases, as well as the impact of next-nearest-neighbor AFM coupling J2 on the transition towards Dirac spin liquid (DSL) phases or stripe order. These references underscore our contribution to the discourse on quantum magnetism in strongly correlated systems and highlight the groundwork laid for future investigations.

2. Extended Discussion on Hubbard Model and Mott Transition: Following the reviewer's advice, we have referenced the suggested articles and expanded our discussion to cover the relevance of our work within this broader research landscape. 

We believe these modifications address the concerns raised and significantly improve the manuscript. We are thankful for the opportunity to refine our work based on the reviewer's insightful feedback.