Strong-coupling approach to the Mott-Hubbard insulator on a Bethe lattice in dynamical mean-field theory

We calculate the Hubbard bands for the half-filled Hubbard model on a Bethe lattice with an infinite coordination number up to and including third order in the inverse Hubbard interaction. We employ the Kato-Takahashi perturbation theory to solve the self-consistency equation of the dynamical mean-field theory analytically for the single-impurity Anderson model in multichain geometry. The weight of the secondary Hubbard sub-bands is of fourth order so that the two-chain geometry is sufficient for our study. Our results for the Mott-Hubbard gap and the density of states of the lower Hubbard band agree very well with those from numerical dynamical density-matrix renormalization group calculations, apart from a resonance contribution at the upper band edge, which cannot be reproduced in low-order perturbation theory.