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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.16834 |
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| _version_ | 1866915819594711040 |
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| author | Hernandez-Cepeda, N. Ulloa, Sergio E. |
| author_facet | Hernandez-Cepeda, N. Ulloa, Sergio E. |
| contents | Quantum dot (QD) platforms have enabled the direct observation of Nagaoka ferromagnetism (NFM) in small arrays and non-infinite interaction strength. However, optimizing the cluster connectivity characteristics that yield a ground state with maximal spin and their robustness against magnetic fields remains unexplored. Employing exact diagonalization of the Hubbard Hamiltonian, we find a connection between the existence of kinetic ferromagnetism and graph theory descriptions. Algebraic connectivity ($λ_2$) and Katz centrality (KC) are shown to be related to the spin-correlation over the system. In square arrays, the onset of NFM is found to be $t_c/U\simeq λ_2^2$. In optimal cluster geometries, large $λ_2$ and low KC fluctuation per site are found to enhance $t_c/U$, extending the NFM phase while diminishing the strength of spin correlation clouds. A perpendicular magnetic field introduces Aharonov-Bohm phases, and a critical flux for which NFM is destroyed. We further find that tuning the flux phase to $π$ results in a ground state that exhibits antiferromagnetic correlations (counter-Nagaoka state). Our results illustrate how NFM and polaron formation can be predicted from the array's connectivity ($λ_2$ and KC), and how the introduction of flux results in the counterintuitive destruction of kinetic ferromagnetism in the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16834 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal array geometries for kinetic magnetism and Nagaoka polarons Hernandez-Cepeda, N. Ulloa, Sergio E. Strongly Correlated Electrons Quantum dot (QD) platforms have enabled the direct observation of Nagaoka ferromagnetism (NFM) in small arrays and non-infinite interaction strength. However, optimizing the cluster connectivity characteristics that yield a ground state with maximal spin and their robustness against magnetic fields remains unexplored. Employing exact diagonalization of the Hubbard Hamiltonian, we find a connection between the existence of kinetic ferromagnetism and graph theory descriptions. Algebraic connectivity ($λ_2$) and Katz centrality (KC) are shown to be related to the spin-correlation over the system. In square arrays, the onset of NFM is found to be $t_c/U\simeq λ_2^2$. In optimal cluster geometries, large $λ_2$ and low KC fluctuation per site are found to enhance $t_c/U$, extending the NFM phase while diminishing the strength of spin correlation clouds. A perpendicular magnetic field introduces Aharonov-Bohm phases, and a critical flux for which NFM is destroyed. We further find that tuning the flux phase to $π$ results in a ground state that exhibits antiferromagnetic correlations (counter-Nagaoka state). Our results illustrate how NFM and polaron formation can be predicted from the array's connectivity ($λ_2$ and KC), and how the introduction of flux results in the counterintuitive destruction of kinetic ferromagnetism in the system. |
| title | Optimal array geometries for kinetic magnetism and Nagaoka polarons |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2512.16834 |