Mott-Hubbard Insulator in Infinite Dimensions
Abstract
We calculate the one-particle density of states for the Mott-Hubbard insulating phase of the Hubbard model on a Bethe lattice in the limit of infinite coordination number. We employ the Kato-Takahashi perturbation theory around the strong-coupling limit to derive the Green function. We show that the Green function for the lower Hubbard band can be expressed in terms of polynomials in the bare hole-hopping operator. We check our technique against the exact solution of the Falicov-Kimball model and give explicit results up to and including second order in the inverse Hubbard interaction. Our results provide a stringent test for analytical and numerical investigations of the Mott-Hubbard insulator and the Mott-Hubbard transition within the dynamical mean-field theory. We find that the Hubbard-III approximation is not satisfactory beyond lowest order, but the local-moment approach provides a very good description of the Mott-Hubbard insulator at strong coupling.
Cite
@article{arxiv.cond-mat/0109535,
title = {Mott-Hubbard Insulator in Infinite Dimensions},
author = {Eva Kalinowski and Florian Gebhard},
journal= {arXiv preprint arXiv:cond-mat/0109535},
year = {2007}
}
Comments
29 pages; accepted for publication in J. Low Temp. Physics; v2: added a factor of two in eqs. (98)-(102); minor changes in Figs. 4+5