Global approximations to correlation functions of strongly interacting quantum field theories

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 Padé 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 $ϕ^4$ field theory and the 2D Hubbard model. For the $ϕ^4$ theory, the resulting two point Padé approximants exhibit uniform and global convergence to the exact correlation function. For the Hubbard model, we show that even at second order, the Padé 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.

💡 Research Summary

The paper introduces a novel framework for constructing global approximations to correlation functions in strongly interacting quantum field theories (QFTs) by interpolating between weak‑coupling and strong‑coupling expansions using a two‑point Padé approximant. Traditional resummation techniques such as one‑point Padé or Borel‑Padé are limited to the vicinity of the origin because the perturbative series has a finite radius of convergence. By contrast, the two‑point Padé method treats the weak‑coupling series (valid for coupling g → 0) and the strong‑coupling series (valid for g → ∞) as two independent “germs” of the target function and builds a rational function that matches a prescribed number of coefficients from each expansion. This converts the extrapolation problem into an interpolation problem, which the authors demonstrate yields uniform and global convergence for all non‑negative coupling values.

The authors first illustrate the idea with the zero‑dimensional φ⁴ integral, where an exact solution is known. They derive the weak‑coupling series by expanding the Gaussian weight and the strong‑coupling series by expanding the quartic term, then construct Padé