SciPost Submission Page
Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers
by Daniel González-Cuadra, Alejandro Bermudez
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Daniel González-Cuadra |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2504.15755v1 (pdf) |
| Date submitted: | June 23, 2025, 11:40 a.m. |
| Submitted by: | Daniel González-Cuadra |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We investigate the emergence of bond-directional spin-spin interactions in a synthetic Fermi-Hubbard bilayer that can be realized with ultracold fermions in Raman optical lattices. The model exploits synthetic dimensions to couple two honeycomb layers, each corresponding to a different hyperfine atomic state, via Raman-assisted tunneling and, moreover, via an inter-layer Hubbard repulsion due to the cold-atom scattering. In the strong-coupling regime at half filling, we derive effective spin Hamiltonians for the kinetic exchange featuring Kitaev, Heisenberg, off-diagonal exchange ($\Gamma$-couplings), as well as tunable Dzyaloshinskii-Moriya interactions. We identify specific configurations that generate both ferromagnetic and antiferromagnetic Kitaev couplings with various perturbations of relevance to Kitaev materials, providing a tunable platform that can explore how quantum spin liquids emerge from itinerant fermion systems. We analyze the Fermi-liquid and Mott-insulating phases, highlighting a correspondence between Dirac and Majorana quasi-particles, with possible phase transitions thereof. In an extreme anisotropic limit, we show that the model reduces to an inter-layer ribbon in a quasi-1D ladder, allowing for a numerical study of the correlated ground state using matrix product states. We find a transition from a symmetry-protected topological insulator to a Kitaev-like regime characterized by nonlocal string order. Our results establish that cold-atom quantum simulators based on Raman optical lattices can be a playground for extended Kitaev models, bridging itinerant fermionic systems and spin-liquid physics.
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
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2025-9-8 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2504.15755v1, delivered 2025-09-08, doi: 10.21468/SciPost.Report.11893
Strengths
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Suggests a new cold atom setting for implementation the physics of Kitaev model
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Various additional terms in the Hamiltonian such as Heisenberg, \Gamma term, DM term emerge naturally from the simple Hubbard model in the strong coupling limit at half-filling.
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The authors present the results of their strong-coupling expansion together with the results of DMRG calculations.
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The authors present a discussion of a possible experimental cold-atom setup.
Weaknesses
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The paper is very lengthy, and it may have been better to use a shorter format .
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The authors make claims (such as discussion of "emergence" in the Introduction), and in their discussion of comparison with other works, which seem to understate previous research in this area.
Report
I find this model quite interesting, and it is also simple, which may allow one to realise and study Kitaev model with additional anisotropies in experiments.
It seems to satisfy acceptance criteria on the point "1. Provides a novel and synergetic link between different research areas." Therefore I recommend the paper for publication with some minor corrections.
Requested changes
- Provide an outline and the summary of the main results in the beginning of the paper. Optionally, shorten the paper and move some of the parts to Appendices.
- Improve Introduction (see Weaknesses)
- Some of the Figures, e.g. 1-4 are very heavy and do not contain much information. Perhaps simplify the figures.
- Check spelling
Recommendation
Publish (meets expectations and criteria for this Journal)
Report #1 by Anonymous (Referee 1) on 2025-7-4 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2504.15755v1, delivered 2025-07-04, doi: 10.21468/SciPost.Report.11513
Strengths
Report
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
We thank both referees for their careful reading of our manuscript and for their positive and constructive comments. We are especially pleased that both referees find our proposal for realizing Kitaev-type physics in cold-atom systems interesting and worthy of publication in SciPost Physics.
Author: Daniel González-Cuadra on 2025-10-27 [id 5956]
(in reply to Report 2 on 2025-09-08)We thank the referee for the careful reading of our manuscript and for considering that it "provides a novel and synergetic link between different research areas". We have addressed the referee's suggestions and revised the manuscript accordingly, and below we answer the referee's points one by one.
We thank the Referee for this suggestions. We have written an extended summary of results at the end of the introduction to clarify the main messages for potential readers. On the other hand, we have decided to maintain the current structure of the paper and avoid adding additional appendices.
There are some works, like the seminal papers previously cited as [15,52] which discuss how the quantum compass spin models do in fact arise from a fermionic model in a Mott insulating regime. What we referred to with "emergence" is to set the focus of attention on the possible critical properties when connecting these string-coupling QSL to the non-interacting metallic or semi-metal phases. It is this second question which was, to the best of our knowledge, far less explored (likely because even the strong-coupling physics with all Kitaev-material terms is already complex enough and not entirely understood) and motivated our work.
Following the Referee's suggestion, we have clarified these differences, and also performed a more exhaustive search in the literature for works discussing the emergence of Kitaev's QSL from a semi-metal as one increases interactions. We have indeed found the following papers that use various mean-field techniques to address this emergence for a particular set of parameters in our model, those that connect to a Kitaev-Heisenberg model
S. R. Hassan, P. V. Sriluckshmy, S. K. Goyal, R. Shankar,and D. Senechal, Phys. Rev. Lett. 110, 037201 (2013).
L. Liang, Z. Wang, and Y. Yu, , Phys. Rev. B 90, 075119 (2014).
[25] J. P. L. Faye, D. Senechal, and S. R. Hassan, Phys. Rev. B 89, 115130 (2014).
More recent papers have addressed this model using tensor network techniques, in partiular projected entangled pairs, and auxiliary-field quantum Monte Carlo, identifying qualitative differences with respect to the mean-field predictions
Shaojun Dong, Hao Zhang, Chao Wang, Meng Zhang, Yong-Jian Han and Lixin He, Chinese Phys. Lett. 40 126403 (2023).
F Mohammadi, SM Tabatabaei, M Kargarian, A Vaezi, Phys. Rev. B 110, 214425 (2024)x
We have included these references in the text, and added a paragraph to discuss the corresponding findings.
We thank the Referee for this suggestion. We would like to note that we already spent a considerable amount of time formatting these figures so that they are rich in content and, yet, visually appealing. We would thus prefer to keep them in the current format.