Brueckner-Goldstone perturbation theory for the half-filled Hubbard model in infinite dimensions

TL;DR

This paper applies Brueckner-Goldstone perturbation theory to compute the ground-state energy and momentum distribution of the half-filled Hubbard model in infinite dimensions, achieving high accuracy and agreement with other methods.

Contribution

It provides the first accurate fourth-order ground-state energy calculation for the model using Brueckner-Goldstone theory, improving upon previous Feynman-Dyson estimates.

Findings

Ground-state energy calculated up to fourth order.

Momentum distribution matches Feynman-Dyson results.

Good agreement with Quantum Monte-Carlo data.

Abstract

We use Brueckner-Goldstone perturbation theory to calculate the ground-state energy of the half-filled Hubbard model in infinite dimensions up to fourth order in the Hubbard interaction. We obtain the momentum distribution as a functional derivative of the ground-state energy with respect to the bare dispersion relation. The resulting expressions agree with those from Rayleigh-Schroedinger perturbation theory. Our results for the momentum distribution and the quasi-particle weight agree very well with those obtained earlier from Feynman-Dyson perturbation theory for the single-particle self-energy. We give the correct fourth-order coefficient in the ground-state energy which was not calculated accurately enough from Feynman-Dyson theory due to the insufficient accuracy of the data for the self-energy, and find a good agreement with recent estimates from Quantum Monte-Carlo calculations.