Time-dependent Gutzwiller theory of pairing fluctuations in the Hubbard model

We present a method to compute pairing fluctuations on top of the Gutzwiller approximation (GA). Our investigations are based on a charge-rotational invariant GA energy functional which is expanded up to second order in the pair fluctuations. Equations of motion for the fluctuations lead to a renormalized ladder-type approximation. Both spectral functions and corrections to static quantities, such as the ground-state energy, are computed. The quality of the method is examined for the single-band Hubbard model, where we compare the dynamical pairing correlations for s- and d-wave symmetries with exact diagonalizations. We find a significant improvement with respect to analogous calculations done within the standard Hartree-Fock ladder approximation. The technique has potential applications in the theory of Auger spectroscopy, superconductivity, and cold atom physics.