Interpolating self-energy of the infinite-dimensional Hubbard model: Modifying the iterative perturbation theory

TL;DR

This paper presents an analytical self-energy expression for the infinite-dimensional Hubbard model, extending iterative perturbation theory to arbitrary fillings and ensuring accuracy in various physical limits.

Contribution

It introduces a generalized iterative perturbation theory for the Hubbard model that is valid across different regimes and reproduces key physical limits accurately.

Findings

Recovers second-order perturbation theory in weak coupling

Exact in the atomic limit

Accurately reproduces spectral density moments

Abstract

We develop an analytical expression for the self-energy of the infinite-dimensional Hubbard model that is correct in a number of different limits. The approach represents a generalization of the iterative perturbation theory to arbitrary fillings. In the weak-coupling regime perturbation theory to second order in the interaction U is recovered. The theory is exact in the atomic limit. The high-energy behavior of the self-energy up to order (1/E)**2 and thereby the first four moments of the spectral density are reproduced correctly. Referring to a standard strong-coupling moment method, we analyze the limit of strong U. Different modifications of the approach are discussed and tested by comparing with the results of an exact diagonalization study.