Numerical observation of $\mathrm{SU}(N)$ Nagaoka ferromagnetism
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916163848503296 |
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| author | Botzung, Thomas Nataf, Pierre |
| author_facet | Botzung, Thomas Nataf, Pierre |
| contents | We provide numerical evidence of the Nagaoka's theorem in the $\mathrm{SU}(N)$ Fermi-Hubbard model on various cluster geometries, such as the square, the honeycomb and the triangular lattices. In particular, by diagonalizing several finite-size clusters, we show that for one hole away from filling $1/N$, the itinerant ferromagnetism arises for $U$ (the positive on-site interaction) larger than $U_c$ (the value at the transition), which strongly depends on the coordination number $z$ and on $N$, the number of degenerate orbitals, that we vary from $N=2$ to $N=6$ in our simulations. We prove that $U_c$ is a non decreasing function of $N$. In addition, we find that the lattice dependency is rooted in the kinetic energy of the hole. We find that large coordination numbers $z$ lower the value of $U_c$. Complementary, we explore the effect of long-range hopping on the appearance of itinerant ferromagnetism and demonstrate that it acts as an increased coordination number, protecting the ferromagnetic phase at small $U$. Finally, both the effects of the presence of some additional holes and of the finite size of the clusters are briefly discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_11588 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical observation of $\mathrm{SU}(N)$ Nagaoka ferromagnetism Botzung, Thomas Nataf, Pierre Strongly Correlated Electrons We provide numerical evidence of the Nagaoka's theorem in the $\mathrm{SU}(N)$ Fermi-Hubbard model on various cluster geometries, such as the square, the honeycomb and the triangular lattices. In particular, by diagonalizing several finite-size clusters, we show that for one hole away from filling $1/N$, the itinerant ferromagnetism arises for $U$ (the positive on-site interaction) larger than $U_c$ (the value at the transition), which strongly depends on the coordination number $z$ and on $N$, the number of degenerate orbitals, that we vary from $N=2$ to $N=6$ in our simulations. We prove that $U_c$ is a non decreasing function of $N$. In addition, we find that the lattice dependency is rooted in the kinetic energy of the hole. We find that large coordination numbers $z$ lower the value of $U_c$. Complementary, we explore the effect of long-range hopping on the appearance of itinerant ferromagnetism and demonstrate that it acts as an increased coordination number, protecting the ferromagnetic phase at small $U$. Finally, both the effects of the presence of some additional holes and of the finite size of the clusters are briefly discussed. |
| title | Numerical observation of $\mathrm{SU}(N)$ Nagaoka ferromagnetism |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2403.11588 |