# 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.

## Key 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.