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Abstract: We present a novel approach that integrates artificial intelligence techniques with quantum field theory to efficiently solve the quantum many-electron problem. Our methodology represents high-order Feynman diagrams as computational graphs with a fractal tensor structure and employs automatic differentiation to implement the higher-order renormalization. This integration of AI technologies with electron field theory enables the efficient computation of many-body correlation functions and vertex functions of the many-electron problem, with potential applications in developing electronic structure theory beyond the one-electron physics.
As a demonstrative application, we apply this AI-driven approach to determine the Coulomb pseudopotential (μ*) in the Eliashberg equation for superconductors. By developing a microscopic theory and leveraging our AI tech stack, we accurately compute μ* from the four-point vertex funtion, elucidating the true strength of the effective Coulomb repulsion between Cooper pairs. Our theory reveals a stronger repulsive force than previously thought, resolving long-standing discrepancies between theory and experiment. The results indicate that metals such as Mg and Na are near a quantum phase transition, providing new insights into the low-temperature superconductivity.