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Mechanism of Superconductivity in the Hubbard Model at Intermediate Interaction Strength

We study the fluctuations responsible for pairing in the $d$-wave superconducting state of the two-dimensional Hubbard model at intermediate coupling within a cluster dynamical mean-field theory with a numerically exact quantum impurity solver. By analyzing how momentum and frequency dependent fluctuations generate the $d-$wave superconducting state in different representations, we identify antiferromagnetic fluctuations as the pairing glue of superconductivity both in the underdoped and the overdoped regime. Nevertheless, in the intermediate coupling regime, the predominant magnetic fluctuations may differ significantly from those described by conventional spin-fluctuation theory.