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

J. M. P. Carmelo

doi:10.1103/p1sc-sx2d

paper

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)]/ $Z_{2}^{2}$ symmetry

arXiv:2604.25712 · doi:10.1103/p1sc-sx2d

Abstract

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.

24 pages, no figures

Exact results for the Hubbard model on bipartite lattices in spatial dimensions d>1: Seven theorems from the full [SU(2)×SU(2)×U(1)]/Z22​ symmetry

Abstract

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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)]/ $Z_{2}^{2}$ symmetry