Evaluation of High Order Terms for the Hubbard Model in the Strong-coupling Limit

The ground-state energy of the Hubbard model on a Bethe lattice with infinite connectivity at half filling is calculated for the insulating phase. Using Kohn's transformation to derive an effective Hamiltonian for the strong-coupling limit, the resulting class of diagrams is determined. We develop an algorithm for an algebraic evaluation of the contributions of high-order terms and check it by applying it to the Falicov-Kimball model that is exactly solvable. For the Hubbard model, the ground-state energy is exactly calculated up to order t^12/U^11. The results of the strong-coupling expansion deviate from numerical calculations as quantum Monte Carlo (or density-matrix renormalization-group) by less than 0.13% (0.32% respectively) for U>4.76.