Global approximations to correlation functions of strongly interacting quantum field theories

TL;DR

This paper presents a novel interpolation method using Padé approximants to construct global correlation functions in strongly interacting quantum field theories, demonstrating promising results on benchmark models.

Contribution

The authors develop a two-point Padé interpolation approach to approximate correlation functions across weak and strong coupling regimes, with proven convergence properties.

Findings

Padé approximants show uniform convergence to exact correlation functions in $\, ext{phi}^4$ theory.

Second-order Padé approximants reasonably characterize the Hubbard model's Green's function.

The method provides a unified approximation across different interaction strengths.

Abstract

We introduce a method for constructing global approximations to correlation functions of strongly interacting quantum field theories, starting from perturbative results. The key idea is to employ interpolation method, such as the two-point Pad\'e expansion, to interpolate the weak and strong coupling expansions of correlation function. We benchmark this many-body interpolation approach on two prototypical models: the lattice $\phi^4$ field theory and the 2D Hubbard model. For the $\phi^4$ theory, the resulting two point Pad\'e approximants exhibit uniform and global convergence to the exact correlation function. For the Hubbard model, we show that even at second order, the Pad\'e appproximant already provides reasonable characterization of the Matsubara Green's function for a wide range of parameters. Finally, we offer a heuristic explanation for these convergence properties based on analytic function theory.