BCS–BEC crossover in one-dimensional integrable model

The crossover from Bardeen–Cooper–Schrieffer (BCS) superfluid with singlet pairs to Bose–Einstein condensation (BEC) of molecules is studied in one dimension. By use of the nested Bethe ansatz method, the ground state properties of spin-1/2 fermions interacting through attractive δ-function are analyzed explicitly for strong and weak couplings. Based on those results, we confirm a crossover picture, that is, in the BEC regime (strong couplings) the system is described by molecules with weak repulsion while in the BCS regime (weak couplings) it behaves as the weakly attractive fermions.