The superfluid transition of 3D attractive Fermi-Hubbard model across BCS-BEC crossover

We propose an iterative numerical approach for solving the three-dimensional attractive Fermi-Hubbard model within the T-matrix approximation, combining with the Fast Fourier Transform (FFT)-accelerated computations.
The FFT is implemented across all momentum directions and the real-frequency domain, enabling the calculation of both single-particle and pair self-energies along with their corresponding spectral functions while preserving full $\bf{k} (\bf{q})$-dependence, a critical feature neglected in conventional local approximation schemes.Our methodology eliminates the need for ad hoc pseudogap approximations, yielding accurate results that successfully reproduce key features of single-particle excitation dynamics observed in state-of-the-art dynamical mean-field theory and quantum Monte Carlo simulations.
Our results reveal that the periodic lattice potential leads to strong local pairing fluctuations illustrated by a prominent pseudogap in the spectral function persisting at elevated temperatures.
For weak and moderate interactions, we demonstrate the presence of Fermi-Liquid (FL) and non-Fermi-Liquid (NFL) regime exhibiting on the phase diagram at high filling and analyze the origin of this behavior and the difference with the situation in the continuous space.
Furthermore, the $\bf{k}$-dependency of self-energy become evident with decreasing temperature, which has a certain impact on the determination of superfluid critical temperature $T_{\rm c}$.