Diagonal Pad\'e Approximant of the one-body Green's function, a study on Hubbard rings

TL;DR

This paper investigates the effectiveness of diagonal Padé approximants in accurately reconstructing the one-body Green's function in many-body physics, using the Hubbard ring model as a test case.

Contribution

It provides empirical evidence supporting the hypothesis that diagonal Padé approximants optimally utilize finite perturbative series for Green's functions.

Findings

Diagonal Padé approximants perform well across various Hubbard ring configurations.

The approach is largely confirmed to be effective for different site numbers, fillings, and interaction strengths.

Supports the use of Padé approximants in many-body Green's function calculations.

Abstract

Pad\'e approximants to the many-body Green's function can be built by rearranging terms of its perturbative expansion. The hypothesis that the best use of a finite number of terms of such an expansion is given by the subclass of diagonal Pad\'e approximants is here tested, and largely confirmed, on a solvable model system, namely the Hubbard ring for a variety of site numbers, fillings and interaction strengths.