Brueckner–Goldstone perturbation theory for the half-filled Hubbard model in infinitedimensions

Abstract

We use Brueckner–Goldstone perturbation theory to calculate the ground-state energy ofthe half-filled Hubbard model in infinite dimensions up to fourth order in the Hubbardinteraction. We obtain the momentum distribution as a functional derivative of theground-state energy with respect to the bare dispersion relation. The resultingexpressions agree with those from Rayleigh–Schrödinger perturbation theory. Ourresults for the momentum distribution and the quasi-particle weight agree verywell with those obtained earlier from Feynman–Dyson perturbation theory forthe single-particle self-energy. We give the correct fourth-order coefficient in theground-state energy which was not calculated accurately enough from Feynman–Dysontheory due to the insufficient accuracy of the data for the self-energy, and find agood agreement with recent estimates from quantum Monte Carlo calculations.