Thermal Phase Structure of the Attractive Fermi Hubbard Model with Imaginary Chemical Potential

We study the BCS--BEC crossover of the large $N$ attractive Fermi-Hubbard model on a one-dimensional lattice using the mean field approximation in the presence of an imaginary chemical potential. We show that the crossover is governed by three parameters. The imaginary chemical potential $iθ$, the temperature via a thermal kernel $g(βE_k,βθ)$ and the parameter $δ_u$ whose sign controls the weak and strong coupling regimes. At the unitarity point ($U=U_c$), we find a thermal window $φ=βθ=2π/3,4π/3$ where the gap vanishes while the fermion number $N_f$, which quantifies the balance between particle-like and hole-like excitations, has a local maximum/minimum. Inside this thermal window BCS and BEC physics are await changes in the coupling to be selected as the dominant regime. We expect that our results will unveil a better understanding of pairing correlations in lattice many-body physics.