HUBBARD-MODEL ON D-DIMENSIONAL HYPERCUBES - EXACT SOLUTION FOR THE 2-ELECTRON CASE

The Hubbard model is exactly solved for two particles on d-dimensional hypercubes. It is shown that the spectrum can be separated into two p arts: a trivial (U-independent) part resulting from symmetries of hype rcubes and a nontrivial part expressed as a single-impurity problem on a set of finite chains of size d'+1 (d'less than or equal to d). The exact expression for the one-particle Green's function is given. Final ly, we discuss the extension of these results to standard hypercubic l attices with periodic boundary conditions.