Hubbard model on d-dimensional hypercubes: Exact solution for the two-electron case

TL;DR

This paper provides an exact solution for the two-electron Hubbard model on d-dimensional hypercubes, revealing a spectrum split into symmetry-driven and impurity-like parts, with implications for hypercubic lattice systems.

Contribution

It introduces an exact analytical solution for the two-electron Hubbard model on hypercubes, including Green's function expressions and spectrum analysis, extending to hypercubic lattices.

Findings

Spectrum separates into symmetry and impurity parts

Exact Green's function derived for two-electron case

Results extend to hypercubic lattices with periodic boundary conditions

Abstract

The Hubbard model is exactly solved for two particles with opposite spins on d-dimensional hypercubes. It is shown that the spectrum can be separated into two parts: a trivial (U-independent) part resulting from symmetries of hypercubes and a non-trivial part expressed as a single-impurity problem on a set of finite chains of size $d^\prime+1$ ($d^\prime \le d$). The exact expression for the one-particle Green's function is given. Finally, we discuss the extension of these results to standard hypercubic lattices with periodic boundary conditions.