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arXiv:2512.18532 · Physical review. B./Physical review. B

Global approximations to correlation functions of strongly interacting quantum field theories

Yuanran Zhu, Yang Yu, Efekan Kökcü, Emanuel Gull, Chao Yang

cond-mat.str-elhep-thquant-phSubmitted Dec 20, 2025• Announced Dec 23, 2025• 0 citations• Revised May 7, 2026 (v3)
v1 · Dec 20, 2025v2 · Feb 18, 2026v3 · May 7, 2026
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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 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.

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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 φ4φ^4φ4 field theory and the 2D Hubbard model. For the φ4φ^4φ4 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.
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