Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\times$SU(2)$\times$U(1)]/$\mathbb{Z}_2^2$ symmetry
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911693645283328 |
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| author | Carmelo, J. M. P. |
| author_facet | Carmelo, J. M. P. |
| contents | There are few exact results for the Hubbard model on bipartite lattices of spatial dimension $d>1$. Nevertheless, the Hubbard model with transfer integral $t$ and onsite repulsion $U$ on bipartite lattices with $N_a$ sites, such as the square, honeycomb, cubic, body-centered cubic, face-centered cubic, and diamond lattices, provides the simplest toy model for describing electronic correlations in many condensed-matter systems and is therefore a quantum problem of considerable physical interest. Seven exact theorems that provide new physical insight into the model are established. Overall, the exact framework based on physical spins and physical $η$-spins for the Hubbard model on bipartite lattices of spatial dimension $d>1$ introduced in this paper offers a robust foundation for future studies of the model, as well as of the condensed-matter materials, such as cuprate superconductors, graphene and graphene-derived systems, and other quantum systems, that it describes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_25712 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\times$SU(2)$\times$U(1)]/$\mathbb{Z}_2^2$ symmetry Carmelo, J. M. P. Strongly Correlated Electrons There are few exact results for the Hubbard model on bipartite lattices of spatial dimension $d>1$. Nevertheless, the Hubbard model with transfer integral $t$ and onsite repulsion $U$ on bipartite lattices with $N_a$ sites, such as the square, honeycomb, cubic, body-centered cubic, face-centered cubic, and diamond lattices, provides the simplest toy model for describing electronic correlations in many condensed-matter systems and is therefore a quantum problem of considerable physical interest. Seven exact theorems that provide new physical insight into the model are established. Overall, the exact framework based on physical spins and physical $η$-spins for the Hubbard model on bipartite lattices of spatial dimension $d>1$ introduced in this paper offers a robust foundation for future studies of the model, as well as of the condensed-matter materials, such as cuprate superconductors, graphene and graphene-derived systems, and other quantum systems, that it describes. |
| title | Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\times$SU(2)$\times$U(1)]/$\mathbb{Z}_2^2$ symmetry |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2604.25712 |