Work

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 ) ] / Z 2 2 symmetry

Year: 2026

Type: article

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.

Source: Physical review. B./Physical review. B

DOI: 10.1103/p1sc-sx2d

Author: J. M. P. Carmelo

Institutions: Universidade do Porto, Instituto Superior Técnico, University of Minho

Language: English

Topic: Physics of Superconductivity and Magnetism

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Universidade do Porto, Universidade do Minho, Fundação para a Ciência e a Tecnologia, Nuclear Fuel Cycle and Supply Chain