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Description

Developing accurate and numerically efficient computational methods for strongly interacting quantum systems remains a central challenge in both high-energy and condensed-matter physics. Compared with fully nonperturbative approaches such as quantum Monte Carlo and DMRG, traditional perturbative techniques remain attractive due to their low-computational cost and favorable scalability to large system sizes. However, the nonconvergence of diagrammatic expansions fundamentally limits their applicability in the strong-correlation regime. This limitation has motivated recent efforts to extend perturbative expansion beyond its radius of convergence using various resummation techniques, with prominent examples including Borel–Padé approximants and approaches inspired by resurgence theory. In this talk, I will introduce a different framework for constructing global approximations to thermodynamic correlation functions in strongly interacting quantum field theories. This approach combines weak- and strong-coupling expansions within an interpolation-based numerical scheme and has proven effective for the lattice φ⁴ field theory and the two-dimensional Hubbard model. Beyond numerical results, I will provide a heuristic explanation for the observed convergence behavior motivated by Lee–Yang theory and analytic continuation.