Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach

Jean Paul Latyr Faye; Oumar Ndiaye; Allé Dioum; Alassane Traoré

doi:doi:10.11648/j.am.20251401.14

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Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach

Jean Paul Latyr Faye^*, Oumar Ndiaye, Allé Dioum, Alassane Traoré

Published in Advances in Materials (Volume 14, Issue 1)

Received: 24 February 2025 Accepted: 17 March 2025 Published: 25 March 2025

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Abstract

Strongly correlated electron systems, where localized magnetic moments interact with conduction electrons, continue to challenge our understanding of quantum phases. In particular, the competition between the Kondo effect-which promotes the formation of singlet states via the screening of localized spins-and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, plays a crucial role in defining the electronic properties of materials such as graphene and other honeycomb lattice systems. In this work, we investigate the interplay between these competing mechanisms using a Kondo-Hubbard model on the hexagonal lattice. Our model incorporates key interactions including the Kondo coupling J_⊥ between conduction electrons and localized spins, the Heisenberg exchange J_H between localized moments, the onsite Coulomb repulsion U for conduction electrons, and a second nearest-neighbor hopping term t′. The study is conducted at half-filling, where each lattice site hosts one electron on average, and the system is analyzed via the variational cluster approximation (VCA) combined with an exact diagonalization solver at zero temperature. Our analysis focuses on mapping the phase diagrams in different parameter spaces, particularly the (J_H, J_⊥) and (J_⊥, UJ_⊥) planes. We find that the antiferromagnetic phase is favored at smaller J_⊥ and larger JH, while an increase in J_⊥ stabilizes the Kondo singlet phase. The transition between these phases occurs smoothly, indicating a second-order phase transition. Additionally, the inclusion of the hopping term t′ is shown to enhance the stability of the Kondo singlet phase. Overall, our results provide new insights into the delicate balance between magnetic order and Kondo singlet formation in low-dimensional correlated systems, potentially guiding future experimental and theoretical investigations in graphene-based materials and related compounds.

Published in	Advances in Materials (Volume 14, Issue 1)
DOI	10.11648/j.am.20251401.14
Page(s)	30-35
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2025. Published by Science Publishing Group

Keywords

Kondo Lattice, Graphene, Variational Cluster Approximation, Magnetic Order, Strong Correlations

References

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APA Style

Faye, J. P. L., Ndiaye, O., Dioum, A., Traoré, A. (2025). Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach. Advances in Materials, 14(1), 30-35. https://doi.org/10.11648/j.am.20251401.14

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ACS Style

Faye, J. P. L.; Ndiaye, O.; Dioum, A.; Traoré, A. Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach. Adv. Mater. 2025, 14(1), 30-35. doi: 10.11648/j.am.20251401.14

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AMA Style

Faye JPL, Ndiaye O, Dioum A, Traoré A. Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach. Adv Mater. 2025;14(1):30-35. doi: 10.11648/j.am.20251401.14

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@article{10.11648/j.am.20251401.14,
  author = {Jean Paul Latyr Faye and Oumar Ndiaye and Allé Dioum and Alassane Traoré},
  title = {Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach},
  journal = {Advances in Materials},
  volume = {14},
  number = {1},
  pages = {30-35},
  doi = {10.11648/j.am.20251401.14},
  url = {https://doi.org/10.11648/j.am.20251401.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.am.20251401.14},
  abstract = {Strongly correlated electron systems, where localized magnetic moments interact with conduction electrons, continue to challenge our understanding of quantum phases. In particular, the competition between the Kondo effect-which promotes the formation of singlet states via the screening of localized spins-and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, plays a crucial role in defining the electronic properties of materials such as graphene and other honeycomb lattice systems. In this work, we investigate the interplay between these competing mechanisms using a Kondo-Hubbard model on the hexagonal lattice. Our model incorporates key interactions including the Kondo coupling J⊥ between conduction electrons and localized spins, the Heisenberg exchange JH between localized moments, the onsite Coulomb repulsion U for conduction electrons, and a second nearest-neighbor hopping term t′. The study is conducted at half-filling, where each lattice site hosts one electron on average, and the system is analyzed via the variational cluster approximation (VCA) combined with an exact diagonalization solver at zero temperature. Our analysis focuses on mapping the phase diagrams in different parameter spaces, particularly the (JH, J⊥) and (J⊥, UJ⊥) planes. We find that the antiferromagnetic phase is favored at smaller J⊥ and larger JH, while an increase in J⊥ stabilizes the Kondo singlet phase. The transition between these phases occurs smoothly, indicating a second-order phase transition. Additionally, the inclusion of the hopping term t′ is shown to enhance the stability of the Kondo singlet phase. Overall, our results provide new insights into the delicate balance between magnetic order and Kondo singlet formation in low-dimensional correlated systems, potentially guiding future experimental and theoretical investigations in graphene-based materials and related compounds. },
 year = {2025}
}

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TY  - JOUR
T1  - Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach
AU  - Jean Paul Latyr Faye
AU  - Oumar Ndiaye
AU  - Allé Dioum
AU  - Alassane Traoré
Y1  - 2025/03/25
PY  - 2025
N1  - https://doi.org/10.11648/j.am.20251401.14
DO  - 10.11648/j.am.20251401.14
T2  - Advances in Materials
JF  - Advances in Materials
JO  - Advances in Materials
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EP  - 35
PB  - Science Publishing Group
SN  - 2327-252X
UR  - https://doi.org/10.11648/j.am.20251401.14
AB  - Strongly correlated electron systems, where localized magnetic moments interact with conduction electrons, continue to challenge our understanding of quantum phases. In particular, the competition between the Kondo effect-which promotes the formation of singlet states via the screening of localized spins-and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, plays a crucial role in defining the electronic properties of materials such as graphene and other honeycomb lattice systems. In this work, we investigate the interplay between these competing mechanisms using a Kondo-Hubbard model on the hexagonal lattice. Our model incorporates key interactions including the Kondo coupling J⊥ between conduction electrons and localized spins, the Heisenberg exchange JH between localized moments, the onsite Coulomb repulsion U for conduction electrons, and a second nearest-neighbor hopping term t′. The study is conducted at half-filling, where each lattice site hosts one electron on average, and the system is analyzed via the variational cluster approximation (VCA) combined with an exact diagonalization solver at zero temperature. Our analysis focuses on mapping the phase diagrams in different parameter spaces, particularly the (JH, J⊥) and (J⊥, UJ⊥) planes. We find that the antiferromagnetic phase is favored at smaller J⊥ and larger JH, while an increase in J⊥ stabilizes the Kondo singlet phase. The transition between these phases occurs smoothly, indicating a second-order phase transition. Additionally, the inclusion of the hopping term t′ is shown to enhance the stability of the Kondo singlet phase. Overall, our results provide new insights into the delicate balance between magnetic order and Kondo singlet formation in low-dimensional correlated systems, potentially guiding future experimental and theoretical investigations in graphene-based materials and related compounds. 
VL  - 14
IS  - 1
ER  -

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Author Information

Jean Paul Latyr Faye

Department of Physics, Faculty of Science and Technology, Cheikh Anta Diop University, Dakar-Fann, Dakar, Senegal

Contact Email
Oumar Ndiaye

Department of Physics, Faculty of Science and Technology, Cheikh Anta Diop University, Dakar-Fann, Dakar, Senegal
Allé Dioum

Department of Physics, Faculty of Science and Technology, Cheikh Anta Diop University, Dakar-Fann, Dakar, Senegal
Alassane Traoré

Department of Physics, Faculty of Science and Technology, Cheikh Anta Diop University, Dakar-Fann, Dakar, Senegal

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APA Style

Faye, J. P. L., Ndiaye, O., Dioum, A., Traoré, A. (2025). Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach. Advances in Materials, 14(1), 30-35. https://doi.org/10.11648/j.am.20251401.14

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ACS Style

Faye, J. P. L.; Ndiaye, O.; Dioum, A.; Traoré, A. Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach. Adv. Mater. 2025, 14(1), 30-35. doi: 10.11648/j.am.20251401.14

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AMA Style

Faye JPL, Ndiaye O, Dioum A, Traoré A. Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach. Adv Mater. 2025;14(1):30-35. doi: 10.11648/j.am.20251401.14

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@article{10.11648/j.am.20251401.14,
  author = {Jean Paul Latyr Faye and Oumar Ndiaye and Allé Dioum and Alassane Traoré},
  title = {Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach},
  journal = {Advances in Materials},
  volume = {14},
  number = {1},
  pages = {30-35},
  doi = {10.11648/j.am.20251401.14},
  url = {https://doi.org/10.11648/j.am.20251401.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.am.20251401.14},
  abstract = {Strongly correlated electron systems, where localized magnetic moments interact with conduction electrons, continue to challenge our understanding of quantum phases. In particular, the competition between the Kondo effect-which promotes the formation of singlet states via the screening of localized spins-and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, plays a crucial role in defining the electronic properties of materials such as graphene and other honeycomb lattice systems. In this work, we investigate the interplay between these competing mechanisms using a Kondo-Hubbard model on the hexagonal lattice. Our model incorporates key interactions including the Kondo coupling J⊥ between conduction electrons and localized spins, the Heisenberg exchange JH between localized moments, the onsite Coulomb repulsion U for conduction electrons, and a second nearest-neighbor hopping term t′. The study is conducted at half-filling, where each lattice site hosts one electron on average, and the system is analyzed via the variational cluster approximation (VCA) combined with an exact diagonalization solver at zero temperature. Our analysis focuses on mapping the phase diagrams in different parameter spaces, particularly the (JH, J⊥) and (J⊥, UJ⊥) planes. We find that the antiferromagnetic phase is favored at smaller J⊥ and larger JH, while an increase in J⊥ stabilizes the Kondo singlet phase. The transition between these phases occurs smoothly, indicating a second-order phase transition. Additionally, the inclusion of the hopping term t′ is shown to enhance the stability of the Kondo singlet phase. Overall, our results provide new insights into the delicate balance between magnetic order and Kondo singlet formation in low-dimensional correlated systems, potentially guiding future experimental and theoretical investigations in graphene-based materials and related compounds. },
 year = {2025}
}

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TY  - JOUR
T1  - Competing Kondo Singlet and Magnetic Order Insulator in Graphene Lattices: A Variational Cluster Approximation Approach
AU  - Jean Paul Latyr Faye
AU  - Oumar Ndiaye
AU  - Allé Dioum
AU  - Alassane Traoré
Y1  - 2025/03/25
PY  - 2025
N1  - https://doi.org/10.11648/j.am.20251401.14
DO  - 10.11648/j.am.20251401.14
T2  - Advances in Materials
JF  - Advances in Materials
JO  - Advances in Materials
SP  - 30
EP  - 35
PB  - Science Publishing Group
SN  - 2327-252X
UR  - https://doi.org/10.11648/j.am.20251401.14
AB  - Strongly correlated electron systems, where localized magnetic moments interact with conduction electrons, continue to challenge our understanding of quantum phases. In particular, the competition between the Kondo effect-which promotes the formation of singlet states via the screening of localized spins-and magnetic ordering driven by the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, plays a crucial role in defining the electronic properties of materials such as graphene and other honeycomb lattice systems. In this work, we investigate the interplay between these competing mechanisms using a Kondo-Hubbard model on the hexagonal lattice. Our model incorporates key interactions including the Kondo coupling J⊥ between conduction electrons and localized spins, the Heisenberg exchange JH between localized moments, the onsite Coulomb repulsion U for conduction electrons, and a second nearest-neighbor hopping term t′. The study is conducted at half-filling, where each lattice site hosts one electron on average, and the system is analyzed via the variational cluster approximation (VCA) combined with an exact diagonalization solver at zero temperature. Our analysis focuses on mapping the phase diagrams in different parameter spaces, particularly the (JH, J⊥) and (J⊥, UJ⊥) planes. We find that the antiferromagnetic phase is favored at smaller J⊥ and larger JH, while an increase in J⊥ stabilizes the Kondo singlet phase. The transition between these phases occurs smoothly, indicating a second-order phase transition. Additionally, the inclusion of the hopping term t′ is shown to enhance the stability of the Kondo singlet phase. Overall, our results provide new insights into the delicate balance between magnetic order and Kondo singlet formation in low-dimensional correlated systems, potentially guiding future experimental and theoretical investigations in graphene-based materials and related compounds. 
VL  - 14
IS  - 1
ER  -

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