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 an interpolation method, such as the two-point Padé expansion, to interpolate between the weak- and strong-coupling expansions of the correlation function. We benchmark this many-body interpolation approach on two prototypical models: the lattice ${\varphi }^4$ field theory and the two-dimensional Hubbard model. For the ${\varphi }^4$ 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 approximant already provides a 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.

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• Finite temperature field theory
• Perturbation theory
• Quantum field theory
• Strongly correlated systems
• Feynman diagrams