First-Order Pairing Transition and Single-Particle Spectral Function in the Attractive Hubbard Model

A dynamical mean-field theory analysis of the attractive Hubbard model in the normal phase is carried out upon restricting to solutions where superconducting order is not allowed. A clear first-order pairing transition as a function of the coupling takes place at all the electron densities out of half filling between a Fermi liquid, stable for $U<\mathrm{}{U}_c$, and an insulating bound pairs phase for $U>\mathrm{}{U}_c$, and it is accompanied by phase separation. The spectral function in the metallic phase is constituted by a low-energy structure around the Fermi level, which disappears discontinuously at ${U=U}_c$, and two high-energy features (Hubbard bands), which persist in the insulating phase.