Fourth-Order Perturbation Theory for the Half-Filled Hubbard Model in Infinite Dimensions

TL;DR

This paper develops a fourth-order perturbation theory approach to analyze the half-filled Hubbard model in infinite dimensions, providing detailed comparisons with other methods and highlighting the strengths and limitations of perturbative and numerical techniques.

Contribution

It introduces a fourth-order perturbation theory calculation for the Hubbard model in infinite dimensions and compares results with various numerical methods, revealing insights into their accuracy and limitations.

Findings

Perturbation theory results agree well with DMFT and DMRG at moderate U/W.

NRG has limited resolution in capturing Hubbard bands.

Iterated Perturbation Theory overestimates quasiparticle weight at higher U/W.

Abstract

We calculate the zero-temperature self-energy to fourth-order perturbation theory in the Hubbard interaction $U$ for the half-filled Hubbard model in infinite dimensions. For the Bethe lattice with bare bandwidth $W$, we compare our perturbative results for the self-energy, the single-particle density of states, and the momentum distribution to those from approximate analytical and numerical studies of the model. Results for the density of states from perturbation theory at $U/W=0.4$ agree very well with those from the Dynamical Mean-Field Theory treated with the Fixed-Energy Exact Diagonalization and with the Dynamical Density-Matrix Renormalization Group. In contrast, our results reveal the limited resolution of the Numerical Renormalization Group approach in treating the Hubbard bands. The momentum distributions from all approximate studies of the model are very similar in the regime where perturbation theory is applicable, $U/W \le 0.6$. Iterated Perturbation Theory overestimates the quasiparticle weight above such moderate interaction strengths.