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

TL;DR

This paper develops an algebraic method to evaluate high-order terms in the strong-coupling expansion of the Hubbard model, achieving highly accurate ground-state energy calculations up to order t^{12}/U^{11}.

Contribution

It introduces an algorithm for algebraic evaluation of high-order terms in the Hubbard model's strong-coupling expansion, validated against exactly solvable models.

Findings

Ground-state energy calculated up to order t^{12}/U^{11}.

Deviations from numerical methods are less than 0.13% for U>4.76.

Method provides highly accurate results in the strong-coupling limit.

Abstract

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.