Evaluation of High Order Terms for the Hubbard Model 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.
Keywords
Cite
@article{arxiv.1106.4938,
title = {Evaluation of High Order Terms for the Hubbard Model in the Strong-coupling Limit},
author = {Eva Kalinowski and Władysław Gluza},
journal= {arXiv preprint arXiv:1106.4938},
year = {2012}
}
Comments
8 pages, 5 figures, 2 flowcharts, 1 table