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The Hubbard model is exactly solved for two particles with opposite spins ond-dimensional hypercubes. It is shown that the spectrum can be separated intotwo parts: a trivial (U-independent) part resulting from symmetries ofhypercubes and a non-trivial part expressed as a single-impurity problem on aset of finite chains of size $d^\prime+1$ ($d^\prime \le d$). The exactexpression for the one-particle Green's function is given. Finally, we discussthe extension of these results to standard hypercubic lattices with periodicboundary conditions.Comment: 5 pages, Latex, with 2 eps figure

physical review. b, condensed matter

Hubbard model on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>−</mml:mo></mml:math>dimensional hypercubes: Exact solution for the two-electron case

Hubbard model ond−dimensional hypercubes: Exact solution for the two-electron case